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                                <div id="anchor-navigation-ex-navbar"><i class="fa fa-navicon"></i><ul><li><span class="title-icon "></span><a href="#&#x8FC1;&#x79FB;&#x5B66;&#x4E60;&#x7814;&#x7A76;&#x7EFC;&#x8FF0;"><b>1. </b>&#x8FC1;&#x79FB;&#x5B66;&#x4E60;&#x7814;&#x7A76;&#x7EFC;&#x8FF0;</a></li><ul><li><span class="title-icon "></span><a href="#&#x5F15;&#x8A00;"><b>1.1. </b>&#x5F15;&#x8A00;</a></li><li><span class="title-icon "></span><a href="#&#x6982;&#x8FF0;"><b>1.2. </b>&#x6982;&#x8FF0;</a></li><ul><li><span class="title-icon "></span><a href="#&#x8FC1;&#x79FB;&#x5B66;&#x4E60;&#x7B80;&#x53F2;"><b>1.2.1. </b>&#x8FC1;&#x79FB;&#x5B66;&#x4E60;&#x7B80;&#x53F2;</a></li><li><span class="title-icon "></span><a href="#&#x7B26;&#x53F7;&#x5B9A;&#x4E49;"><b>1.2.2. </b>&#x7B26;&#x53F7;&#x5B9A;&#x4E49;</a></li><li><span class="title-icon "></span><a href="#&#x8FC1;&#x79FB;&#x5B66;&#x4E60;&#x6280;&#x672F;&#x7684;&#x5206;&#x7C7B;"><b>1.2.3. </b>&#x8FC1;&#x79FB;&#x5B66;&#x4E60;&#x6280;&#x672F;&#x7684;&#x5206;&#x7C7B;</a></li></ul><li><span class="title-icon "></span><a href="#&#x5F52;&#x7EB3;&#x8FC1;&#x79FB;&#x5B66;&#x4E60;"><b>1.3. </b>&#x5F52;&#x7EB3;&#x8FC1;&#x79FB;&#x5B66;&#x4E60;</a></li><ul><li><span class="title-icon "></span><a href="#&#x4F20;&#x9012;&#x5B9E;&#x4F8B;&#x7684;&#x77E5;&#x8BC6;"><b>1.3.1. </b>&#x4F20;&#x9012;&#x5B9E;&#x4F8B;&#x7684;&#x77E5;&#x8BC6;</a></li><li><span class="title-icon "></span><a href="#&#x4F20;&#x9012;&#x7279;&#x5F81;&#x8868;&#x793A;&#x7684;&#x77E5;&#x8BC6;"><b>1.3.2. </b>&#x4F20;&#x9012;&#x7279;&#x5F81;&#x8868;&#x793A;&#x7684;&#x77E5;&#x8BC6;</a></li><li><span class="title-icon "></span><a href="#&#x4F20;&#x9012;&#x53C2;&#x6570;&#x77E5;&#x8BC6;"><b>1.3.3. </b>&#x4F20;&#x9012;&#x53C2;&#x6570;&#x77E5;&#x8BC6;</a></li><li><span class="title-icon "></span><a href="#&#x4F20;&#x9012;&#x5173;&#x7CFB;&#x77E5;&#x8BC6;"><b>1.3.4. </b>&#x4F20;&#x9012;&#x5173;&#x7CFB;&#x77E5;&#x8BC6;</a></li></ul><li><span class="title-icon "></span><a href="#&#x8F6C;&#x5BFC;&#x8FC1;&#x79FB;&#x5B66;&#x4E60;"><b>1.4. </b>&#x8F6C;&#x5BFC;&#x8FC1;&#x79FB;&#x5B66;&#x4E60;</a></li><ul><li><span class="title-icon "></span><a href="#&#x5B9E;&#x4F8B;&#x77E5;&#x8BC6;&#x7684;&#x8F6C;&#x79FB;"><b>1.4.1. </b>&#x5B9E;&#x4F8B;&#x77E5;&#x8BC6;&#x7684;&#x8F6C;&#x79FB;</a></li><li><span class="title-icon "></span><a href="#&#x4F20;&#x9012;&#x7279;&#x5F81;&#x8868;&#x793A;&#x7684;&#x77E5;&#x8BC6;_1"><b>1.4.2. </b>&#x4F20;&#x9012;&#x7279;&#x5F81;&#x8868;&#x793A;&#x7684;&#x77E5;&#x8BC6;</a></li></ul><li><span class="title-icon "></span><a href="#&#x65E0;&#x76D1;&#x7763;&#x8FC1;&#x79FB;&#x5B66;&#x4E60;"><b>1.5. </b>&#x65E0;&#x76D1;&#x7763;&#x8FC1;&#x79FB;&#x5B66;&#x4E60;</a></li><ul><li><span class="title-icon "></span><a href="#&#x8FC1;&#x79FB;&#x7279;&#x5F81;&#x8868;&#x793A;&#x7684;&#x77E5;&#x8BC6;"><b>1.5.1. </b>&#x8FC1;&#x79FB;&#x7279;&#x5F81;&#x8868;&#x793A;&#x7684;&#x77E5;&#x8BC6;</a></li></ul><li><span class="title-icon "></span><a href="#&#x8F6C;&#x79FB;&#x754C;&#x9650;&#x548C;&#x8D1F;&#x8F6C;&#x79FB;"><b>1.6. </b>&#x8F6C;&#x79FB;&#x754C;&#x9650;&#x548C;&#x8D1F;&#x8F6C;&#x79FB;</a></li><li><span class="title-icon "></span><a href="#&#x603B;&#x7ED3;"><b>1.7. </b>&#x603B;&#x7ED3;</a></li></ul></ul></div><a href="#&#x8FC1;&#x79FB;&#x5B66;&#x4E60;&#x7814;&#x7A76;&#x7EFC;&#x8FF0;" id="anchorNavigationExGoTop"><i class="fa fa-arrow-up"></i></a><div class="treeview__container"><div class="treeview__container-title"><span class="treeview__main-title">Treeview</span><span class="treeview__copyright">Copyright &#xA9; aleen42 all right reserved, powered by <a href="https://github.com/aleen42" target="_blank">aleen42</a></span></div><ul>
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<li><div><a href="#&#x603B;&#x7ED3;">&#x603B;&#x7ED3;</a><i></i></div></li>
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<p>[TOC]</p>
<h1 id="&#x8FC1;&#x79FB;&#x5B66;&#x4E60;&#x7814;&#x7A76;&#x7EFC;&#x8FF0;"><a name="&#x8FC1;&#x79FB;&#x5B66;&#x4E60;&#x7814;&#x7A76;&#x7EFC;&#x8FF0;" class="anchor-navigation-ex-anchor" href="#&#x8FC1;&#x79FB;&#x5B66;&#x4E60;&#x7814;&#x7A76;&#x7EFC;&#x8FF0;"><i class="fa fa-link" aria-hidden="true"></i></a>1. &#x8FC1;&#x79FB;&#x5B66;&#x4E60;&#x7814;&#x7A76;&#x7EFC;&#x8FF0;</h1>
<blockquote>
<p>&#x91CD;&#x70B9;&#x662F;&#x5206;&#x7C7B;&#x5F53;&#x524D;&#x8FC1;&#x79FB;&#x5B66;&#x4E60;&#x7684;&#x5206;&#x7C7B;&#x3001;&#x56DE;&#x5F52;&#x548C;&#x805A;&#x7C7B;&#x95EE;&#x9898;&#x3002; &#x672C;&#x6587;&#x8BA8;&#x8BBA;&#x4E86;&#x8FC1;&#x79FB;&#x5B66;&#x4E60;&#x4E0E;&#x9886;&#x57DF;&#x81EA;&#x9002;&#x5E94;&#x3001;&#x591A;&#x4EFB;&#x52A1;&#x5B66;&#x4E60;&#x3001;&#x6837;&#x672C;&#x9009;&#x62E9;&#x504F;&#x5DEE;&#x3001;&#x534F;&#x53D8;&#x91CF;&#x8F6C;&#x79FB;&#x7B49;&#x76F8;&#x5173;&#x673A;&#x5668;&#x5B66;&#x4E60;&#x6280;&#x672F;&#x4E4B;&#x95F4;&#x7684;&#x5173;&#x7CFB; </p>
</blockquote>
<h2 id="&#x5F15;&#x8A00;"><a name="&#x5F15;&#x8A00;" class="anchor-navigation-ex-anchor" href="#&#x5F15;&#x8A00;"><i class="fa fa-link" aria-hidden="true"></i></a>1.1. &#x5F15;&#x8A00;</h2>
<p>&#x76EE;&#x6807;&#xFF1A;&#x5C06;&#x4E00;&#x4E2A;&#x5904;&#x5728;&#x6E90;&#x57DF;&#x4E0A;&#x7684;&#x6A21;&#x578B;&#x7528;&#x5728;&#x76EE;&#x6807;&#x57DF;&#x4E0A;&#x7684;&#x6A21;&#x578B;&#x4E0A;</p>
<h2 id="&#x6982;&#x8FF0;"><a name="&#x6982;&#x8FF0;" class="anchor-navigation-ex-anchor" href="#&#x6982;&#x8FF0;"><i class="fa fa-link" aria-hidden="true"></i></a>1.2. &#x6982;&#x8FF0;</h2>
<h3 id="&#x8FC1;&#x79FB;&#x5B66;&#x4E60;&#x7B80;&#x53F2;"><a name="&#x8FC1;&#x79FB;&#x5B66;&#x4E60;&#x7B80;&#x53F2;" class="anchor-navigation-ex-anchor" href="#&#x8FC1;&#x79FB;&#x5B66;&#x4E60;&#x7B80;&#x53F2;"><i class="fa fa-link" aria-hidden="true"></i></a>1.2.1. &#x8FC1;&#x79FB;&#x5B66;&#x4E60;&#x7B80;&#x53F2;</h3>
<ol>
<li>&#x8FC1;&#x79FB;&#x5B66;&#x4E60;&#x7684;&#x65B0;&#x804C;&#x8D23;&#xFF1A;&#x7CFB;&#x7EDF;&#x8BC6;&#x522B;&#x5E76;&#x5E94;&#x7528;&#x4ECE;&#x4EE5;&#x524D;&#x4EFB;&#x52A1;&#x4E2D;&#x5B66;&#x4E60;&#x5230;&#x7684;&#x77E5;&#x8BC6;&#x6216;&#x6280;&#x80FD;&#x5230;&#x65B0;&#x4EFB;&#x52A1;&#x7684;&#x80FD;&#x529B;&#xFF08;&#x65E8;&#x5728;&#x4ECE;&#x4E00;&#x4E2A;&#x6216;&#x591A;&#x4E2A;&#x6E90;&#x4EFB;&#x52A1;&#x4E2D;&#x63D0;&#x53D6;&#x77E5;&#x8BC6;&#xFF09;</li>
<li>&#x76F8;&#x6BD4;&#x4E8E;&#x591A;&#x4EFB;&#x52A1;&#x5B66;&#x4E60;&#xFF0C;&#x5B83;&#x66F4;&#x52A0;&#x6CE8;&#x91CD;&#x4E8E;&#x76EE;&#x6807;&#x4EFB;&#x52A1;</li>
</ol>
<h3 id="&#x7B26;&#x53F7;&#x5B9A;&#x4E49;"><a name="&#x7B26;&#x53F7;&#x5B9A;&#x4E49;" class="anchor-navigation-ex-anchor" href="#&#x7B26;&#x53F7;&#x5B9A;&#x4E49;"><i class="fa fa-link" aria-hidden="true"></i></a>1.2.2. &#x7B26;&#x53F7;&#x5B9A;&#x4E49;</h3>
<ul>
<li>&#x6E90;&#x57DF;<span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>D</mi></mrow><annotation encoding="application/x-tex">D</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height:0.68333em;"></span><span class="strut bottom" style="height:0.68333em;vertical-align:0em;"></span><span class="base textstyle uncramped"><span class="mord mathit" style="margin-right:0.02778em;">D</span></span></span></span>&#xFF1A;&#x5305;&#x542B;&#x4E86;&#x7279;&#x5F81;&#x7A7A;&#x95F4; <span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>&#x3C7;</mi></mrow><annotation encoding="application/x-tex">\chi</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height:0.43056em;"></span><span class="strut bottom" style="height:0.625em;vertical-align:-0.19444em;"></span><span class="base textstyle uncramped"><span class="mord mathit">&#x3C7;</span></span></span></span>&#x548C;&#x8FB9;&#x7F18;&#x5206;&#x5E03;&#x6982;&#x7387;<span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>P</mi><mo>(</mo><mi>&#x3C7;</mi><mo>)</mo></mrow><annotation encoding="application/x-tex">P(\chi)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height:0.75em;"></span><span class="strut bottom" style="height:1em;vertical-align:-0.25em;"></span><span class="base textstyle uncramped"><span class="mord mathit" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord mathit">&#x3C7;</span><span class="mclose">)</span></span></span></span>, &#x4F8B;&#x5982;<span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>&#x3C7;</mi></mrow><annotation encoding="application/x-tex">\chi</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height:0.43056em;"></span><span class="strut bottom" style="height:0.625em;vertical-align:-0.19444em;"></span><span class="base textstyle uncramped"><span class="mord mathit">&#x3C7;</span></span></span></span>&#x662F;&#x6240;&#x6709;&#x6837;&#x672C;&#x7684;&#x7A7A;&#x95F4;&#xFF0C;<span class="katex"><span class="katex-mathml"><math><semantics><mrow><msub><mi>&#x3C7;</mi><mi>i</mi></msub></mrow><annotation encoding="application/x-tex">\chi_i</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height:0.43056em;"></span><span class="strut bottom" style="height:0.625em;vertical-align:-0.19444em;"></span><span class="base textstyle uncramped"><span class="mord"><span class="mord mathit">&#x3C7;</span><span class="msupsub"><span class="vlist"><span style="top:0.15em;margin-right:0.05em;margin-left:0em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle cramped mtight"><span class="mord mathit mtight">i</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span></span></span></span>&#x662F;&#x67D0;&#x4E00;&#x4E9B;&#x6837;&#x672C;&#x7684;&#x5BF9;&#x5E94;&#x7684;&#x5411;&#x91CF;&#xFF0C;<span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>X</mi></mrow><annotation encoding="application/x-tex">X</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height:0.68333em;"></span><span class="strut bottom" style="height:0.68333em;vertical-align:0em;"></span><span class="base textstyle uncramped"><span class="mord mathit" style="margin-right:0.07847em;">X</span></span></span></span>&#x5219;&#x662F;&#x4E00;&#x4E2A;&#x7279;&#x5B9A;&#x7684;&#x5B66;&#x4E60;&#x6837;&#x672C;&#x3002;&#x7ED9;&#x5B9A;&#x4E00;&#x4E2A;&#x6E90;&#x57DF;<span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>D</mi><mo>=</mo><mo fence="false">(</mo><mi>&#x3C7;</mi><mo separator="true">,</mo><mi>P</mi><mo>(</mo><mi>&#x3C7;</mi><mo>)</mo><mo>)</mo></mrow><annotation encoding="application/x-tex">D=\big( \chi,P(\chi))</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height:0.85em;"></span><span class="strut bottom" style="height:1.20001em;vertical-align:-0.35001em;"></span><span class="base textstyle uncramped"><span class="mord mathit" style="margin-right:0.02778em;">D</span><span class="mrel">=</span><span class="mord style-wrap reset-textstyle textstyle uncramped"><span class="delimsizing size1">(</span></span><span class="mord mathit">&#x3C7;</span><span class="mpunct">,</span><span class="mord mathit" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord mathit">&#x3C7;</span><span class="mclose">)</span><span class="mclose">)</span></span></span></span>&#xFF0C;&#x6BCF;&#x4E2A;&#x4EFB;&#x52A1;&#x5305;&#x62EC;&#x4E24;&#x4E2A;&#x90E8;&#x5206;&#xFF1A;&#x6807;&#x7B7E;&#x57DF;<span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>y</mi></mrow><annotation encoding="application/x-tex">y</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height:0.43056em;"></span><span class="strut bottom" style="height:0.625em;vertical-align:-0.19444em;"></span><span class="base textstyle uncramped"><span class="mord mathit" style="margin-right:0.03588em;">y</span></span></span></span> &#x548C;&#x9884;&#x6D4B;&#x51FD;&#x6570;<span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>f</mi><mo>(</mo><mo>)</mo></mrow><annotation encoding="application/x-tex">f()</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height:0.75em;"></span><span class="strut bottom" style="height:1em;vertical-align:-0.25em;"></span><span class="base textstyle uncramped"><span class="mord mathit" style="margin-right:0.10764em;">f</span><span class="mopen">(</span><span class="mclose">)</span></span></span></span>,&#x6BCF;&#x4E00;&#x4E2A;&#x8BAD;&#x7EC3;&#x5BF9;&#x8C61;&#x90FD;&#x5305;&#x62EC;&#x4E86;<span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo>(</mo><msub><mi>x</mi><mi>i</mi></msub><mo separator="true">,</mo><msub><mi>y</mi><mi>i</mi></msub><mo>)</mo></mrow><annotation encoding="application/x-tex">(x_i,y_i)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height:0.75em;"></span><span class="strut bottom" style="height:1em;vertical-align:-0.25em;"></span><span class="base textstyle uncramped"><span class="mopen">(</span><span class="mord"><span class="mord mathit">x</span><span class="msupsub"><span class="vlist"><span style="top:0.15em;margin-right:0.05em;margin-left:0em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle cramped mtight"><span class="mord mathit mtight">i</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span><span class="mpunct">,</span><span class="mord"><span class="mord mathit" style="margin-right:0.03588em;">y</span><span class="msupsub"><span class="vlist"><span style="top:0.15em;margin-right:0.05em;margin-left:-0.03588em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle cramped mtight"><span class="mord mathit mtight">i</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span><span class="mclose">)</span></span></span></span>&#x3002;&#x4ECE;&#x6982;&#x7387;&#x7684;&#x89C2;&#x70B9;&#x6765;&#x770B;<span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo></mrow><annotation encoding="application/x-tex">f(x)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height:0.75em;"></span><span class="strut bottom" style="height:1em;vertical-align:-0.25em;"></span><span class="base textstyle uncramped"><span class="mord mathit" style="margin-right:0.10764em;">f</span><span class="mopen">(</span><span class="mord mathit">x</span><span class="mclose">)</span></span></span></span>&#x53EF;&#x4EE5;&#x88AB;&#x5199;&#x4E3A;<span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>P</mi><mo>(</mo><mi>y</mi><mi mathvariant="normal">&#x2223;</mi><mi>x</mi><mo>)</mo></mrow><annotation encoding="application/x-tex">P(y|x)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height:0.75em;"></span><span class="strut bottom" style="height:1em;vertical-align:-0.25em;"></span><span class="base textstyle uncramped"><span class="mord mathit" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord mathit" style="margin-right:0.03588em;">y</span><span class="mord mathrm">&#x2223;</span><span class="mord mathit">x</span><span class="mclose">)</span></span></span></span></li>
<li><strong>&#x5B9A;&#x4E49;1(&#x8FC1;&#x79FB;&#x5B66;&#x4E60;)</strong>&#xFF1A;&#x7ED9;&#x5B9A;&#x6E90;&#x57DF;<span class="katex"><span class="katex-mathml"><math><semantics><mrow><msub><mi>D</mi><mi>S</mi></msub></mrow><annotation encoding="application/x-tex">D_S</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height:0.68333em;"></span><span class="strut bottom" style="height:0.83333em;vertical-align:-0.15em;"></span><span class="base textstyle uncramped"><span class="mord"><span class="mord mathit" style="margin-right:0.02778em;">D</span><span class="msupsub"><span class="vlist"><span style="top:0.15em;margin-right:0.05em;margin-left:-0.02778em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle cramped mtight"><span class="mord mathit mtight" style="margin-right:0.05764em;">S</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span></span></span></span>&#x548C;&#x5B66;&#x4E60;&#x4EFB;&#x52A1;<span class="katex"><span class="katex-mathml"><math><semantics><mrow><msub><mi>T</mi><mi>s</mi></msub></mrow><annotation encoding="application/x-tex">T_s</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height:0.68333em;"></span><span class="strut bottom" style="height:0.83333em;vertical-align:-0.15em;"></span><span class="base textstyle uncramped"><span class="mord"><span class="mord mathit" style="margin-right:0.13889em;">T</span><span class="msupsub"><span class="vlist"><span style="top:0.15em;margin-right:0.05em;margin-left:-0.13889em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle cramped mtight"><span class="mord mathit mtight">s</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span></span></span></span>&#xFF0C;&#x76EE;&#x6807;&#x57DF;<span class="katex"><span class="katex-mathml"><math><semantics><mrow><msub><mi>D</mi><mi>T</mi></msub></mrow><annotation encoding="application/x-tex">D_T</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height:0.68333em;"></span><span class="strut bottom" style="height:0.83333em;vertical-align:-0.15em;"></span><span class="base textstyle uncramped"><span class="mord"><span class="mord mathit" style="margin-right:0.02778em;">D</span><span class="msupsub"><span class="vlist"><span style="top:0.15em;margin-right:0.05em;margin-left:-0.02778em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle cramped mtight"><span class="mord mathit mtight" style="margin-right:0.13889em;">T</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span></span></span></span> &#x548C;&#x5B66;&#x4E60;&#x4EFB;&#x52A1;<span class="katex"><span class="katex-mathml"><math><semantics><mrow><msub><mi>T</mi><mi>T</mi></msub></mrow><annotation encoding="application/x-tex">T_T</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height:0.68333em;"></span><span class="strut bottom" style="height:0.83333em;vertical-align:-0.15em;"></span><span class="base textstyle uncramped"><span class="mord"><span class="mord mathit" style="margin-right:0.13889em;">T</span><span class="msupsub"><span class="vlist"><span style="top:0.15em;margin-right:0.05em;margin-left:-0.13889em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle cramped mtight"><span class="mord mathit mtight" style="margin-right:0.13889em;">T</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span></span></span></span>&#xFF0C;&#x8FC1;&#x79FB;&#x5B66;&#x4E60;&#x65E8;&#x5728;&#x4F7F;&#x7528;<span class="katex"><span class="katex-mathml"><math><semantics><mrow><msub><mi>D</mi><mi>S</mi></msub></mrow><annotation encoding="application/x-tex">D_S</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height:0.68333em;"></span><span class="strut bottom" style="height:0.83333em;vertical-align:-0.15em;"></span><span class="base textstyle uncramped"><span class="mord"><span class="mord mathit" style="margin-right:0.02778em;">D</span><span class="msupsub"><span class="vlist"><span style="top:0.15em;margin-right:0.05em;margin-left:-0.02778em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle cramped mtight"><span class="mord mathit mtight" style="margin-right:0.05764em;">S</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span></span></span></span>&#x548C;<span class="katex"><span class="katex-mathml"><math><semantics><mrow><msub><mi>T</mi><mi>S</mi></msub></mrow><annotation encoding="application/x-tex">T_S</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height:0.68333em;"></span><span class="strut bottom" style="height:0.83333em;vertical-align:-0.15em;"></span><span class="base textstyle uncramped"><span class="mord"><span class="mord mathit" style="margin-right:0.13889em;">T</span><span class="msupsub"><span class="vlist"><span style="top:0.15em;margin-right:0.05em;margin-left:-0.13889em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle cramped mtight"><span class="mord mathit mtight" style="margin-right:0.05764em;">S</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span></span></span></span>&#x4E2D;&#x7684;&#x77E5;&#x8BC6;&#xFF0C;&#x5E2E;&#x52A9;&#x4F18;&#x5316;&#x5728;<span class="katex"><span class="katex-mathml"><math><semantics><mrow><msub><mi>D</mi><mi>T</mi></msub></mrow><annotation encoding="application/x-tex">D_T</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height:0.68333em;"></span><span class="strut bottom" style="height:0.83333em;vertical-align:-0.15em;"></span><span class="base textstyle uncramped"><span class="mord"><span class="mord mathit" style="margin-right:0.02778em;">D</span><span class="msupsub"><span class="vlist"><span style="top:0.15em;margin-right:0.05em;margin-left:-0.02778em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle cramped mtight"><span class="mord mathit mtight" style="margin-right:0.13889em;">T</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span></span></span></span>&#x4E2D;&#x7684;&#x9884;&#x6D4B;&#x51FD;&#x6570;<span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>f</mi><mo>(</mo><mo>)</mo></mrow><annotation encoding="application/x-tex">f()</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height:0.75em;"></span><span class="strut bottom" style="height:1em;vertical-align:-0.25em;"></span><span class="base textstyle uncramped"><span class="mord mathit" style="margin-right:0.10764em;">f</span><span class="mopen">(</span><span class="mclose">)</span></span></span></span>&#x3002;</li>
<li>&#x5728;&#x4E0A;&#x9762;&#x7684;&#x5B9A;&#x4E49;&#x4E2D;<span class="katex"><span class="katex-mathml"><math><semantics><mrow><msub><mi>D</mi><mi>s</mi></msub><mo>&#x2260;</mo><msub><mi>D</mi><mi>t</mi></msub></mrow><annotation encoding="application/x-tex">D_s \neq D_t</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height:0.716em;"></span><span class="strut bottom" style="height:0.9309999999999999em;vertical-align:-0.215em;"></span><span class="base textstyle uncramped"><span class="mord"><span class="mord mathit" style="margin-right:0.02778em;">D</span><span class="msupsub"><span class="vlist"><span style="top:0.15em;margin-right:0.05em;margin-left:-0.02778em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle cramped mtight"><span class="mord mathit mtight">s</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span><span class="mrel">&#x2260;</span><span class="mord"><span class="mord mathit" style="margin-right:0.02778em;">D</span><span class="msupsub"><span class="vlist"><span style="top:0.15em;margin-right:0.05em;margin-left:-0.02778em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle cramped mtight"><span class="mord mathit mtight">t</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span></span></span></span>&#xFF0C;&#x610F;&#x5473;&#x7740;&#x6E90;&#x57DF;&#x548C;&#x76EE;&#x6807;&#x57DF;&#x7684;&#x7279;&#x5F81;&#x7A7A;&#x95F4;&#x4E0D;&#x540C;&#x6216;&#x8FB9;&#x7F18;&#x5206;&#x5E03;&#x6982;&#x7387;&#x51FD;&#x6570;&#x4E0D;&#x76F8;&#x540C;; &#x5F53;<span class="katex"><span class="katex-mathml"><math><semantics><mrow><msub><mi>T</mi><mi>s</mi></msub><mo>&#x2260;</mo><msub><mi>T</mi><mi>t</mi></msub></mrow><annotation encoding="application/x-tex">T_s \neq T_t</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height:0.716em;"></span><span class="strut bottom" style="height:0.9309999999999999em;vertical-align:-0.215em;"></span><span class="base textstyle uncramped"><span class="mord"><span class="mord mathit" style="margin-right:0.13889em;">T</span><span class="msupsub"><span class="vlist"><span style="top:0.15em;margin-right:0.05em;margin-left:-0.13889em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle cramped mtight"><span class="mord mathit mtight">s</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span><span class="mrel">&#x2260;</span><span class="mord"><span class="mord mathit" style="margin-right:0.13889em;">T</span><span class="msupsub"><span class="vlist"><span style="top:0.15em;margin-right:0.05em;margin-left:-0.13889em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle cramped mtight"><span class="mord mathit mtight">t</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span></span></span></span> &#x5219;&#x610F;&#x5473;&#x7740;&#x6807;&#x7B7E;&#x7A7A;&#x95F4;&#x4E0D;&#x540C;&#x6216;&#x6761;&#x4EF6;&#x8FB9;&#x7F18;&#x5206;&#x5E03;&#x6982;&#x7387;&#x4E0D;&#x540C;</li>
<li>&#x82E5;&#x6E90;&#x57DF;&#x548C;&#x76EE;&#x6807;&#x57DF;&#x7684;&#x7279;&#x5F81;&#x7A7A;&#x95F4;&#x5B58;&#x5728;&#x67D0;&#x79CD;&#x663E;&#x5F0F;&#x6216;&#x9690;&#x5F0F;&#x7684;&#x5173;&#x7CFB;&#xFF0C;&#x6211;&#x4EEC;&#x5219;&#x79F0;&#x4ED6;&#x4EEC;&#x76F8;&#x5173;&#x3002;</li>
</ul>
<h3 id="&#x8FC1;&#x79FB;&#x5B66;&#x4E60;&#x6280;&#x672F;&#x7684;&#x5206;&#x7C7B;"><a name="&#x8FC1;&#x79FB;&#x5B66;&#x4E60;&#x6280;&#x672F;&#x7684;&#x5206;&#x7C7B;" class="anchor-navigation-ex-anchor" href="#&#x8FC1;&#x79FB;&#x5B66;&#x4E60;&#x6280;&#x672F;&#x7684;&#x5206;&#x7C7B;"><i class="fa fa-link" aria-hidden="true"></i></a>1.2.3. &#x8FC1;&#x79FB;&#x5B66;&#x4E60;&#x6280;&#x672F;&#x7684;&#x5206;&#x7C7B;</h3>
<ol>
<li><p>&#x4E09;&#x4E2A;&#x95EE;&#x9898;&#xFF08;&#x8FC1;&#x79FB;&#x4EC0;&#x4E48;&#xFF0C;&#x5982;&#x4F55;&#x8FC1;&#x79FB;&#xFF0C;&#x4F55;&#x65F6;&#x8FC1;&#x79FB;&#xFF09;&#xFF1A;</p>
<ul>
<li><p>&#x8FC1;&#x79FB;&#x4EC0;&#x4E48;</p>
<p>&#x6709;&#x4E9B;&#x77E5;&#x8BC6;&#x5728;&#x4E0D;&#x540C;&#x57DF;&#x4E4B;&#x95F4;&#x53EF;&#x80FD;&#x662F;&#x901A;&#x7528;&#x7684;</p>
</li>
<li><p>&#x4F55;&#x65F6;&#x8FC1;&#x79FB;</p>
<p>&#x5E94;&#x5F53;&#x955C;&#x50CF;&#x6280;&#x80FD;&#x8F6C;&#x79FB;&#xFF0C;&#x6709;&#x4E9B;&#x65F6;&#x5019;&#x77E5;&#x8BC6;&#x4E0D;&#x5E94;&#x8BE5;&#x88AB;&#x8F6C;&#x79FB;&#xFF08;&#x8D1F;&#x8FC1;&#x79FB;&#xFF09;</p>
</li>
</ul>
</li>
<li><p>&#x4E09;&#x79CD;&#x8FC1;&#x79FB;&#x5B66;&#x4E60;
<img src="../images/1618906971406.png" alt="1618906971406"></p>
<ol>
<li>&#x5728;&#x5F52;&#x7EB3;&#x8FC1;&#x79FB;&#x5B66;&#x4E60;&#x8BBE;&#x7F6E;&#x4E2D;&#xFF0C;&#x76EE;&#x6807;&#x4EFB;&#x52A1;&#x4E0D;&#x540C;&#x57DF;&#x6E90;&#x4EFB;&#x52A1;&#xFF0C;&#x6B64;&#x65F6;&#x9700;&#x4ECE;&#x76EE;&#x6807;&#x57DF;&#x4E2D;&#x9009;&#x53D6;&#x4E00;&#x4E9B;&#x6807;&#x8BB0;&#x6570;&#x636E;&#x6765;&#x63A8;&#x65AD;&#x5BA2;&#x89C2;&#x9884;&#x6D4B;&#x6A21;&#x578B;<ul>
<li>&#x5F53;&#x6E90;&#x57DF;&#x4E2D;&#x6709;&#x5F88;&#x591A;&#x6570;&#x636E;&#x662F;&#x53EF;&#x7528;&#x7684;&#x65F6;&#xFF0C;&#x5F52;&#x7EB3;&#x8FC1;&#x79FB;&#x5B66;&#x4E60;&#x8BBE;&#x7F6E;&#x7C7B;&#x4F3C;&#x4E8E;&#x591A;&#x4EFB;&#x52A1;&#x5B66;&#x4E60;&#x8BBE;&#x7F6E;</li>
<li>&#x6CA1;&#x6709;&#x53EF;&#x7528;&#x6570;&#x636E;&#x65F6;&#xFF0C;&#x5E94;&#x91C7;&#x7528;&#x81EA;&#x5B66;&#x8BBE;&#x7F6E;&#x3002;</li>
</ul>
</li>
<li>&#x5728;&#x8F6C;&#x5BFC;&#x8FC1;&#x79FB;&#x5B66;&#x4E60;&#x8BBE;&#x7F6E;&#x4E2D;&#xFF0C;&#x6E90;&#x4EFB;&#x52A1;&#x4E0E;&#x76EE;&#x6807;&#x4EFB;&#x52A1;&#x76F8;&#x540C;&#xFF0C;&#x4F46;&#x6E90;&#x57DF;&#x4E0E;&#x76EE;&#x6807;&#x57DF;&#x4E0D;&#x540C;&#x3002;&#x6B64;&#x65F6;&#x76EE;&#x6807;&#x57DF;&#x4E2D;&#x6CA1;&#x6709;&#x6570;&#x636E;&#x53EF;&#x7528;&#x3002;&#x6B64;&#x65F6;&#x6709;&#x4E24;&#x79CD;&#x60C5;&#x51B5;&#x3002;<ul>
<li>&#x6E90;&#x57DF;&#x548C;&#x76EE;&#x6807;&#x57DF;&#x7684;&#x7279;&#x5F81;&#x7A7A;&#x95F4;&#x4E0D;&#x540C;</li>
<li>&#x7279;&#x5F81;&#x7A7A;&#x95F4;&#x76F8;&#x540C;&#xFF0C;&#x4F46;&#x8FB9;&#x7F18;&#x5206;&#x5E03;&#x6982;&#x7387;&#x4E0D;&#x540C;&#x3002;</li>
</ul>
</li>
<li>&#x5728;&#x65E0;&#x76D1;&#x7763;&#x8FC1;&#x79FB;&#x5B66;&#x4E60;&#x8BBE;&#x7F6E;&#x4E2D;&#xFF0C;&#x76EE;&#x6807;&#x4EFB;&#x52A1;&#x4E0E;&#x6E90;&#x4EFB;&#x52A1;&#x4E0D;&#x540C;&#x4F46;&#x76F8;&#x5173;&#x3002;&#x6B64;&#x65F6;&#x6CA1;&#x6709;&#x53EF;&#x7528;&#x7684;&#x6570;&#x636E;</li>
</ol>
</li>
<li><p>&#x4EE5;&#x4E0A;&#x4E09;&#x79CD;&#x60C5;&#x51B5;&#x7684;&#x603B;&#x7ED3;
<img src="../images/1618907822531.png" alt="1618907822531">
<img src="../images/1618907926866.png" alt="1618907926866"></p>
<blockquote>
<p>&#x7B2C;&#x4E00;&#x79CD;&#x60C5;&#x51B5;&#x53EF;&#x4EE5;&#x88AB;&#x79F0;&#x4E3A;&#x57FA;&#x4E8E;&#x5B9E;&#x4F8B;&#x7684;&#x8FC1;&#x79FB;&#x5B66;&#x4E60;&#xFF0C;&#x7B2C;&#x4E8C;&#x79CD;&#x662F;&#x7279;&#x5F81;&#x8868;&#x793A;&#x8F6C;&#x79FB;&#x65B9;&#x6CD5;&#xFF0C;&#x7B2C;&#x4E09;&#x79CD;&#x662F;&#x53C2;&#x6570;&#x8F6C;&#x79FB;&#x65B9;&#x6CD5;&#xFF0C;&#x6700;&#x540E;&#x4E00;&#x79CD;&#x60C5;&#x51B5;&#x53EF;&#x4EE5;&#x88AB;&#x79F0;&#x4E3A;&#x5173;&#x7CFB;&#x53EA;&#x662F;&#x8F6C;&#x79FB;&#x65B9;&#x6CD5;&#x3002;</p>
</blockquote>
</li>
<li><p>&#x4E0B;&#x8868;&#x662F;&#x5BF9;&#x51E0;&#x7C7B;&#x8FC1;&#x79FB;&#x5B66;&#x4E60;&#x65B9;&#x6CD5;&#x7684;&#x603B;&#x7ED3;
<img src="../images/1618908245640.png" alt="1618908245640">
<img src="../images/1618908291498.png" alt="1618908291498"></p>
</li>
</ol>
<h2 id="&#x5F52;&#x7EB3;&#x8FC1;&#x79FB;&#x5B66;&#x4E60;"><a name="&#x5F52;&#x7EB3;&#x8FC1;&#x79FB;&#x5B66;&#x4E60;" class="anchor-navigation-ex-anchor" href="#&#x5F52;&#x7EB3;&#x8FC1;&#x79FB;&#x5B66;&#x4E60;"><i class="fa fa-link" aria-hidden="true"></i></a>1.3. &#x5F52;&#x7EB3;&#x8FC1;&#x79FB;&#x5B66;&#x4E60;</h2>
<ol>
<li><strong>&#x5B9A;&#x4E49;2(&#x5F52;&#x7EB3;&#x8FC1;&#x79FB;&#x5B66;&#x4E60;)</strong>&#xFF1A;&#x7ED9;&#x5B9A;&#x6E90;&#x57DF; <span class="katex"><span class="katex-mathml"><math><semantics><mrow><msub><mi>D</mi><mi>S</mi></msub></mrow><annotation encoding="application/x-tex">D_S</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height:0.68333em;"></span><span class="strut bottom" style="height:0.83333em;vertical-align:-0.15em;"></span><span class="base textstyle uncramped"><span class="mord"><span class="mord mathit" style="margin-right:0.02778em;">D</span><span class="msupsub"><span class="vlist"><span style="top:0.15em;margin-right:0.05em;margin-left:-0.02778em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle cramped mtight"><span class="mord mathit mtight" style="margin-right:0.05764em;">S</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span></span></span></span> &#x548C;&#x5B66;&#x4E60;&#x4EFB;&#x52A1; <span class="katex"><span class="katex-mathml"><math><semantics><mrow><msub><mi>T</mi><mi>S</mi></msub></mrow><annotation encoding="application/x-tex">T_S</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height:0.68333em;"></span><span class="strut bottom" style="height:0.83333em;vertical-align:-0.15em;"></span><span class="base textstyle uncramped"><span class="mord"><span class="mord mathit" style="margin-right:0.13889em;">T</span><span class="msupsub"><span class="vlist"><span style="top:0.15em;margin-right:0.05em;margin-left:-0.13889em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle cramped mtight"><span class="mord mathit mtight" style="margin-right:0.05764em;">S</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span></span></span></span> ,&#x76EE;&#x6807;&#x57DF; <span class="katex"><span class="katex-mathml"><math><semantics><mrow><msub><mi>D</mi><mi>T</mi></msub></mrow><annotation encoding="application/x-tex"> D_T </annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height:0.68333em;"></span><span class="strut bottom" style="height:0.83333em;vertical-align:-0.15em;"></span><span class="base textstyle uncramped"><span class="mord"><span class="mord mathit" style="margin-right:0.02778em;">D</span><span class="msupsub"><span class="vlist"><span style="top:0.15em;margin-right:0.05em;margin-left:-0.02778em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle cramped mtight"><span class="mord mathit mtight" style="margin-right:0.13889em;">T</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span></span></span></span> &#x548C; <span class="katex"><span class="katex-mathml"><math><semantics><mrow><msub><mi>T</mi><mi>T</mi></msub></mrow><annotation encoding="application/x-tex"> T_T </annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height:0.68333em;"></span><span class="strut bottom" style="height:0.83333em;vertical-align:-0.15em;"></span><span class="base textstyle uncramped"><span class="mord"><span class="mord mathit" style="margin-right:0.13889em;">T</span><span class="msupsub"><span class="vlist"><span style="top:0.15em;margin-right:0.05em;margin-left:-0.13889em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle cramped mtight"><span class="mord mathit mtight" style="margin-right:0.13889em;">T</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span></span></span></span> &#xFF0C;&#x5F52;&#x7EB3;&#x8FC1;&#x79FB;&#x5B66;&#x4E60;&#x65E8;&#x5728;&#x7528;&#x5728; <span class="katex"><span class="katex-mathml"><math><semantics><mrow><msub><mi>D</mi><mi>S</mi></msub></mrow><annotation encoding="application/x-tex">D_S </annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height:0.68333em;"></span><span class="strut bottom" style="height:0.83333em;vertical-align:-0.15em;"></span><span class="base textstyle uncramped"><span class="mord"><span class="mord mathit" style="margin-right:0.02778em;">D</span><span class="msupsub"><span class="vlist"><span style="top:0.15em;margin-right:0.05em;margin-left:-0.02778em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle cramped mtight"><span class="mord mathit mtight" style="margin-right:0.05764em;">S</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span></span></span></span> &#x548C; <span class="katex"><span class="katex-mathml"><math><semantics><mrow><msub><mi>T</mi><mi>S</mi></msub></mrow><annotation encoding="application/x-tex">T_S</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height:0.68333em;"></span><span class="strut bottom" style="height:0.83333em;vertical-align:-0.15em;"></span><span class="base textstyle uncramped"><span class="mord"><span class="mord mathit" style="margin-right:0.13889em;">T</span><span class="msupsub"><span class="vlist"><span style="top:0.15em;margin-right:0.05em;margin-left:-0.13889em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle cramped mtight"><span class="mord mathit mtight" style="margin-right:0.05764em;">S</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span></span></span></span> &#x4E0A;&#x7684;&#x77E5;&#x8BC6;&#x4F18;&#x5316;&#x5728;<span class="katex"><span class="katex-mathml"><math><semantics><mrow><msub><mi>D</mi><mi>T</mi></msub></mrow><annotation encoding="application/x-tex"> D_T </annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height:0.68333em;"></span><span class="strut bottom" style="height:0.83333em;vertical-align:-0.15em;"></span><span class="base textstyle uncramped"><span class="mord"><span class="mord mathit" style="margin-right:0.02778em;">D</span><span class="msupsub"><span class="vlist"><span style="top:0.15em;margin-right:0.05em;margin-left:-0.02778em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle cramped mtight"><span class="mord mathit mtight" style="margin-right:0.13889em;">T</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span></span></span></span>&#x4E0A;&#x76EE;&#x6807;&#x68C0;&#x6D4B;&#x51FD;&#x6570;<span class="katex"><span class="katex-mathml"><math><semantics><mrow><msub><mi>f</mi><mi>T</mi></msub><mo>(</mo><mo>)</mo></mrow><annotation encoding="application/x-tex"> f_T() </annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height:0.75em;"></span><span class="strut bottom" style="height:1em;vertical-align:-0.25em;"></span><span class="base textstyle uncramped"><span class="mord"><span class="mord mathit" style="margin-right:0.10764em;">f</span><span class="msupsub"><span class="vlist"><span style="top:0.15em;margin-right:0.05em;margin-left:-0.10764em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle cramped mtight"><span class="mord mathit mtight" style="margin-right:0.13889em;">T</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span><span class="mopen">(</span><span class="mclose">)</span></span></span></span></li>
<li>&#x5927;&#x591A;&#x6570;&#x8FC1;&#x79FB;&#x5B66;&#x4E60;&#x65B9;&#x6CD5;&#x503E;&#x5411;&#x4E8E;&#x5E94;&#x7528;&#x4E8E;&#x6E90;&#x57DF;&#x4E2D;&#x7684;&#x6807;&#x8BB0;&#x6570;&#x636E;&#x53EF;&#x7528;</li>
</ol>
<h3 id="&#x4F20;&#x9012;&#x5B9E;&#x4F8B;&#x7684;&#x77E5;&#x8BC6;"><a name="&#x4F20;&#x9012;&#x5B9E;&#x4F8B;&#x7684;&#x77E5;&#x8BC6;" class="anchor-navigation-ex-anchor" href="#&#x4F20;&#x9012;&#x5B9E;&#x4F8B;&#x7684;&#x77E5;&#x8BC6;"><i class="fa fa-link" aria-hidden="true"></i></a>1.3.1. &#x4F20;&#x9012;&#x5B9E;&#x4F8B;&#x7684;&#x77E5;&#x8BC6;</h3>
<ol>
<li><code>boosting</code>&#x7B97;&#x6CD5;<code>TrAdaBoost</code>&#xFF1A;&#x5047;&#x5B9A;&#x6E90;&#x57DF;&#x3001;&#x76EE;&#x6807;&#x57DF;&#x4E2D;&#x4F7F;&#x7528;&#x4E86;&#x5B8C;&#x5168;&#x76F8;&#x540C;&#x7684;&#x6570;&#x636E;&#xFF0C;&#x4F46;&#x5206;&#x5E03;&#x4E0D;&#x540C;&#x3002;&#x5B83;&#x8BD5;&#x56FE;&#x4FEE;&#x6539;&#x6E90;&#x57DF;&#x6570;&#x636E;&#x7684;&#x52A0;&#x6743;&#xFF0C;&#x9F13;&#x52B1;&#x201C;&#x597D;&#x201D;&#x6570;&#x636E;&#xFF0C;&#x51CF;&#x5C11;&#x201C;&#x574F;&#x201D;&#x6570;&#x636E;&#x7684;&#x5F71;&#x54CD;&#xFF1B;&#x8BEF;&#x5DEE;&#x4EC5;&#x5728;&#x76EE;&#x6807;&#x6570;&#x636E;&#x4E0A;&#x8BA1;&#x7B97;</li>
</ol>
<h3 id="&#x4F20;&#x9012;&#x7279;&#x5F81;&#x8868;&#x793A;&#x7684;&#x77E5;&#x8BC6;"><a name="&#x4F20;&#x9012;&#x7279;&#x5F81;&#x8868;&#x793A;&#x7684;&#x77E5;&#x8BC6;" class="anchor-navigation-ex-anchor" href="#&#x4F20;&#x9012;&#x7279;&#x5F81;&#x8868;&#x793A;&#x7684;&#x77E5;&#x8BC6;"><i class="fa fa-link" aria-hidden="true"></i></a>1.3.2. &#x4F20;&#x9012;&#x7279;&#x5F81;&#x8868;&#x793A;&#x7684;&#x77E5;&#x8BC6;</h3>
<p>&#x627E;&#x5230;&#x597D;&#x7684; &#x7279;&#x5F81;&#x8868;&#x793A;&#x53EF;&#x4EE5;&#x6700;&#x5C0F;&#x5316;&#x9886;&#x57DF;&#x8BEF;&#x5DEE;&#x548C;&#x5206;&#x7C7B;/&#x56DE;&#x5F52;&#x6A21;&#x578B;&#x8BEF;&#x5DEE;&#x3002;&#x5BF9;&#x4E8E;&#x4E0D;&#x540C;&#x7684;&#x6E90;&#x57DF;&#x6570;&#x636E;&#xFF0C;&#x5BFB;&#x627E;&#x7279;&#x5F81;&#x8868;&#x793A;&#x7684;&#x7B56;&#x7565;&#x4E0D;&#x540C;&#x3002;</p>
<ol>
<li>&#x5F53;&#x6709;&#x5927;&#x91CF;&#x6807;&#x8BB0;&#x6570;&#x636E;&#x53EF;&#x7528;&#x65F6;&#xFF0C;&#x4F7F;&#x7528;&#x76D1;&#x7763;&#x5B66;&#x4E60;&#x65B9;&#x6CD5;&#x6765;&#x6784;&#x5EFA;&#x7279;&#x5F81;&#x8868;&#x793A;</li>
<li>&#x82E5;&#x6CA1;&#x6709;&#xFF0C;&#x5219;&#x4F7F;&#x7528;&#x65E0;&#x76D1;&#x7763;&#x5B66;&#x4E60;&#x65B9;&#x6CD5;&#x3002;</li>
</ol>
<h4 id="&#x6709;&#x76D1;&#x7763;&#x7279;&#x5F81;&#x6784;&#x5EFA;"><a name="&#x6709;&#x76D1;&#x7763;&#x7279;&#x5F81;&#x6784;&#x5EFA;" class="anchor-navigation-ex-anchor" href="#&#x6709;&#x76D1;&#x7763;&#x7279;&#x5F81;&#x6784;&#x5EFA;"><i class="fa fa-link" aria-hidden="true"></i></a>&#x6709;&#x76D1;&#x7763;&#x7279;&#x5F81;&#x6784;&#x5EFA;</h4>
<p>&#x8FD9;&#x91CC;&#x7528;&#x5230;&#x7684;&#x65B9;&#x6CD5;&#x7C7B;&#x4F3C;&#x4E8E;&#x591A;&#x4EFB;&#x52A1;&#x5B66;&#x4E60;&#x4E2D;&#x4F7F;&#x7528;&#x7684;&#x65B9;&#x6CD5;&#x3002;</p>
<ul>
<li><p>&#x57FA;&#x672C;&#x601D;&#x60F3;&#xFF1A;&#x5B66;&#x4E60;&#x4E00;&#x4E2A;&#x53EF;&#x4EE5;&#x5728;&#x76F8;&#x5173;&#x4EFB;&#x52A1;&#x91CC;&#x5171;&#x4EAB;&#x7684;&#x4F4E;&#x7EF4;&#x8868;&#x793A;&#x3002;</p>
</li>
<li><p>&#x6027;&#x7684;&#x8868;&#x793A;&#x65B9;&#x6CD5;&#x53EF;&#x4EE5;&#x51CF;&#x5C11;&#x6BCF;&#x4E2A;&#x4EFB;&#x52A1;&#x7684;&#x5206;&#x7C7B;&#x6216;&#x56DE;&#x5F52;&#x6A21;&#x578B;&#x8BEF;&#x5DEE;</p>
</li>
<li><p><code>Argyrious</code>&#x7B49;&#x4EBA;&#x63D0;&#x51FA;&#x4E86;&#x4E00;&#x79CD;&#x591A;&#x4EFB;&#x52A1;&#x5B66;&#x4E60;&#x7684;&#x7A00;&#x758F;&#x7279;&#x5F81;&#x5B66;&#x4E60;&#x65B9;&#x6CD5;&#xFF0C;&#x5728;&#x5F52;&#x7EB3;&#x8FC1;&#x79FB;&#x5B66;&#x4E60;&#x8BBE;&#x7F6E;&#x4E2D;&#xFF0C;&#x53EF;&#x4EE5;&#x901A;&#x8FC7;&#x4E00;&#x4E2A;&#x4F18;&#x5316;&#x95EE;&#x9898;&#x6765;&#x5B66;&#x4E60;&#x5E38;&#x89C1;&#x7279;&#x5F81;</p>
</li>
</ul>
<pre><code> argminA,U&#x2211;t&#x2208;{T,S}&#x2211;i=1ntL(yti,&#x27E8;at,UTxti&#x27E9;)+&#x3B3;&#x2223;&#x2223;A&#x2223;&#x2223;2,12s.t.U&#x2208;Od
     \begin{aligned}
  &amp;{arg \min}_{A,U} \sum\limits_{t\in\{T,S\}} \sum\limits_{i=1}^{n_t} {L(y_{t_i},\langle a_t,U^Tx_{t_i}\rangle)+\gamma {||A||}_{2,1}^2} \\ 
  &amp; s.t. \qquad U \in {O}^d 
  \end{aligned}
  &#x200B;&#x200B;&#x200B;&#x200B;&#x200B;argmin&#x200B;A,U&#x200B;&#x200B;&#x200B;t&#x2208;{T,S}&#x200B;&#x2211;&#x200B;&#x200B;&#x200B;i=1&#x200B;&#x2211;&#x200B;n&#x200B;t&#x200B;&#x200B;&#x200B;&#x200B;L(y&#x200B;t&#x200B;i&#x200B;&#x200B;&#x200B;&#x200B;,&#x27E8;a&#x200B;t&#x200B;&#x200B;,U&#x200B;T&#x200B;&#x200B;x&#x200B;t&#x200B;i&#x200B;&#x200B;&#x200B;&#x200B;&#x27E9;)+&#x3B3;&#x2223;&#x2223;A&#x2223;&#x2223;&#x200B;2,1&#x200B;2&#x200B;&#x200B;&#x200B;s.t.U&#x2208;O&#x200B;d&#x200B;&#x200B;&#x200B;&#x200B;
</code></pre><blockquote>
<p>A&#x662F;&#x4E00;&#x4E2A;&#x53C2;&#x6570;&#x77E9;&#x9635;&#xFF0C;U&#x662F;&#x4E00;&#x4E2A;d*d&#x7684;&#x6620;&#x5C04;&#x51FD;&#x6570;&#xFF0C;&#x7528;&#x4E8E;&#x5C06;&#x539F;&#x59CB;&#x9AD8;&#x4F4D;&#x6570;&#x636E;&#x4F4E;&#x7EF4;&#x5316;&#xFF1B;<span class="katex"><span class="katex-mathml"><math><semantics><mrow><msub><mrow><mi mathvariant="normal">&#x2223;</mi><mi mathvariant="normal">&#x2223;</mi><mi>A</mi><mi mathvariant="normal">&#x2223;</mi><mi mathvariant="normal">&#x2223;</mi></mrow><mrow><mi>r</mi><mo separator="true">,</mo><mi>p</mi></mrow></msub><mo>:</mo><mo>=</mo><mo>(</mo><msubsup><mo>&#x2211;</mo><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mi>d</mi></msubsup><msubsup><mrow><mi mathvariant="normal">&#x2223;</mi><mi mathvariant="normal">&#x2223;</mi><msup><mi>a</mi><mi>i</mi></msup><mi mathvariant="normal">&#x2223;</mi><mi mathvariant="normal">&#x2223;</mi></mrow><mi>t</mi><mi>p</mi></msubsup><msup><mo>)</mo><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><mi>p</mi></mrow></mfrac></mrow></msup></mrow><annotation encoding="application/x-tex">{||A||}_{r,p}:=(\sum\limits_{i=1}^d{||a^i||}_t^p)^{\frac{1}{p}}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height:1.5361130000000003em;"></span><span class="strut bottom" style="height:2.513782em;vertical-align:-0.9776689999999999em;"></span><span class="base textstyle uncramped"><span class="mord"><span class="mord textstyle uncramped"><span class="mord mathrm">&#x2223;</span><span class="mord mathrm">&#x2223;</span><span class="mord mathit">A</span><span class="mord mathrm">&#x2223;</span><span class="mord mathrm">&#x2223;</span></span><span class="msupsub"><span class="vlist"><span style="top:0.29999999999999993em;margin-right:0.05em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle cramped mtight"><span class="mord scriptstyle cramped mtight"><span class="mord mathit mtight" style="margin-right:0.02778em;">r</span><span class="mpunct mtight">,</span><span class="mord mathit mtight">p</span></span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span><span class="mrel">:</span><span class="mrel">=</span><span class="mopen">(</span><span class="mop op-limits"><span class="vlist"><span style="top:0.8776689999999999em;margin-left:0em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle cramped mtight"><span class="mord scriptstyle cramped mtight"><span class="mord mathit mtight">i</span><span class="mrel mtight">=</span><span class="mord mathrm mtight">1</span></span></span></span><span style="top:-0.000005000000000088267em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span><span class="mop op-symbol small-op">&#x2211;</span></span></span><span style="top:-0.9500050000000002em;margin-left:0em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle uncramped mtight"><span class="mord mathit mtight">d</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span><span class="mord"><span class="mord textstyle uncramped"><span class="mord mathrm">&#x2223;</span><span class="mord mathrm">&#x2223;</span><span class="mord"><span class="mord mathit">a</span><span class="msupsub"><span class="vlist"><span style="top:-0.363em;margin-right:0.05em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle uncramped mtight"><span class="mord mathit mtight">i</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span><span class="mord mathrm">&#x2223;</span><span class="mord mathrm">&#x2223;</span></span><span class="msupsub"><span class="vlist"><span style="top:0.3em;margin-right:0.05em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle cramped mtight"><span class="mord mathit mtight">t</span></span></span><span style="top:-0.43866399999999994em;margin-right:0.05em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle uncramped mtight"><span class="mord mathit mtight">p</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span><span class="mclose"><span class="mclose">)</span><span class="msupsub"><span class="vlist"><span style="top:-0.44576999999999994em;margin-right:0.05em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle uncramped mtight"><span class="mord scriptstyle uncramped mtight"><span class="mord reset-scriptstyle scriptstyle uncramped mtight"><span class="mopen sizing reset-size5 size5 reset-scriptstyle textstyle uncramped nulldelimiter"></span><span class="mfrac"><span class="vlist"><span style="top:0.344em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-scriptstyle scriptscriptstyle cramped mtight"><span class="mord scriptscriptstyle cramped mtight"><span class="mord mathit mtight">p</span></span></span></span><span style="top:-0.22142857142857142em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-scriptstyle textstyle uncramped frac-line"></span></span><span style="top:-0.384em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-scriptstyle scriptscriptstyle uncramped mtight"><span class="mord scriptscriptstyle uncramped mtight"><span class="mord mathrm mtight">1</span></span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span><span class="mclose sizing reset-size5 size5 reset-scriptstyle textstyle uncramped nulldelimiter"></span></span></span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span></span></span></span>&#xFF1B;&#x4F18;&#x5316;&#x95EE;&#x9898;&#xFF08;1&#xFF09;&#x53EF;&#x4EE5;&#x8F6C;&#x5316;&#x4E3A;&#x7B49;&#x4EF7;&#x7684;&#x51F8;&#x4F18;&#x5316;&#x516C;&#x5F0F;</p>
</blockquote>
<ul>
<li><p>&#x540E;&#x7EED;&#x7684;&#x5DE5;&#x4F5C;</p>
<ul>
<li>&#x63D0;&#x51FA;&#x4E86;&#x591A;&#x4EFB;&#x52A1;&#x7ED3;&#x6784;&#x5B66;&#x4E60;&#x7684;&#x77E9;&#x9635;&#x6B63;&#x5219;&#x5316;&#x6846;&#x67B6;&#xFF1B;</li>
<li>&#x63D0;&#x51FA;&#x4E86;&#x4E00;&#x79CD;&#x51F8;&#x4F18;&#x5316;&#x7B97;&#x6CD5;&#xFF0C;&#x4ECE;&#x9884;&#x6D4B;&#x4EFB;&#x52A1;&#x7684;&#x96C6;&#x5408;&#x4E2D;&#x540C;&#x65F6;&#x5B66;&#x4E60;&#x5143;&#x5148;&#x9A8C;&#x548C;&#x7279;&#x5F81;&#x6743;&#x91CD;&#xFF1B;</li>
<li>&#x63D0;&#x51FA;&#x4E86;&#x7528;SVMs&#x9009;&#x62E9;&#x591A;&#x4EFB;&#x52A1;&#x5B66;&#x4E60;&#x7684;&#x7279;&#x5F81;</li>
<li>&#x8BBE;&#x8BA1;&#x4E86;&#x4E00;&#x79CD;&#x57FA;&#x4E8E;&#x5185;&#x6838;&#x7684;&#x5F52;&#x7EB3;&#x4F20;&#x8F93;&#x65B9;&#x6CD5;</li>
</ul>
</li>
</ul>
<h4 id="&#x65E0;&#x76D1;&#x7763;&#x7279;&#x5F81;&#x6784;&#x5EFA;"><a name="&#x65E0;&#x76D1;&#x7763;&#x7279;&#x5F81;&#x6784;&#x5EFA;" class="anchor-navigation-ex-anchor" href="#&#x65E0;&#x76D1;&#x7763;&#x7279;&#x5F81;&#x6784;&#x5EFA;"><i class="fa fa-link" aria-hidden="true"></i></a>&#x65E0;&#x76D1;&#x7763;&#x7279;&#x5F81;&#x6784;&#x5EFA;</h4>
<ul>
<li><p>&#x6709;&#x4EBA;&#x63D0;&#x51FA;&#x4E86;&#x7A00;&#x758F;&#x7F16;&#x7801;&#xFF0C;&#x7528;&#x4EE5;&#x5B66;&#x4E60;&#x9AD8;&#x7EA7;&#x522B;&#x7684;&#x7279;&#x5F81;&#x3002;&#x8FD9;&#x91CC;&#x6709;&#x4E24;&#x4E2A;&#x6B65;&#x9AA4;&#xFF1A;</p>
<ol>
<li><p>&#x901A;&#x8FC7;&#x5728;&#x6E90;&#x57DF;&#x6570;&#x636E;&#x4E0A;&#x89E3;&#x51B3;&#x5982;&#x4E0B;&#x7684;&#x4F18;&#x5316;&#x95EE;&#x9898;&#x800C;&#x4EA7;&#x751F;&#x4E86;&#x9AD8;&#x9636;&#x57FA;&#x5411;&#x91CF;<span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>b</mi><mo>=</mo><mo>{</mo><msub><mi>b</mi><mn>1</mn></msub><mo separator="true">,</mo><msub><mi>b</mi><mn>2</mn></msub><mo separator="true">,</mo><mi mathvariant="normal">.</mi><mi mathvariant="normal">.</mi><mi mathvariant="normal">.</mi><mo separator="true">,</mo><msub><mi>b</mi><mi>s</mi></msub><mo>}</mo></mrow><annotation encoding="application/x-tex">b=\{b_1,b_2,...,b_s\}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height:0.75em;"></span><span class="strut bottom" style="height:1em;vertical-align:-0.25em;"></span><span class="base textstyle uncramped"><span class="mord mathit">b</span><span class="mrel">=</span><span class="mopen">{</span><span class="mord"><span class="mord mathit">b</span><span class="msupsub"><span class="vlist"><span style="top:0.15em;margin-right:0.05em;margin-left:0em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle cramped mtight"><span class="mord mathrm mtight">1</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span><span class="mpunct">,</span><span class="mord"><span class="mord mathit">b</span><span class="msupsub"><span class="vlist"><span style="top:0.15em;margin-right:0.05em;margin-left:0em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle cramped mtight"><span class="mord mathrm mtight">2</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span><span class="mpunct">,</span><span class="mord mathrm">.</span><span class="mord mathrm">.</span><span class="mord mathrm">.</span><span class="mpunct">,</span><span class="mord"><span class="mord mathit">b</span><span class="msupsub"><span class="vlist"><span style="top:0.15em;margin-right:0.05em;margin-left:0em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle cramped mtight"><span class="mord mathit mtight">s</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span><span class="mclose">}</span></span></span></span>
<span class="katex"><span class="katex-mathml"><math><semantics><mrow><mtable><mtr><mtd><mrow><msub><mi>min</mi><mrow><mi>a</mi><mo separator="true">,</mo><mi>b</mi></mrow></msub><msub><mo>&#x2211;</mo><mrow><mi>i</mi></mrow></msub><mi mathvariant="normal">&#x2223;</mi><mi mathvariant="normal">&#x2223;</mi><msub><mi>x</mi><mrow><msub><mi>S</mi><mi>i</mi></msub></mrow></msub><mo>&#x2212;</mo><msub><mo>&#x2211;</mo><mi>j</mi></msub><mrow><msubsup><mi>a</mi><mrow><msub><mi>S</mi><mi>i</mi></msub></mrow><mi>j</mi></msubsup><msub><mi>b</mi><mi>j</mi></msub></mrow><mi mathvariant="normal">&#x2223;</mi><msubsup><mi mathvariant="normal">&#x2223;</mi><mn>2</mn><mn>2</mn></msubsup><mo>+</mo><mi>&#x3B2;</mi><mi mathvariant="normal">&#x2223;</mi><mi mathvariant="normal">&#x2223;</mi><msub><mi>a</mi><mrow><msub><mi>S</mi><mi>i</mi></msub></mrow></msub><mi mathvariant="normal">&#x2223;</mi><msub><mi mathvariant="normal">&#x2223;</mi><mn>1</mn></msub></mrow></mtd></mtr><mtr><mtd><mrow><mi>s</mi><mi mathvariant="normal">.</mi><mi>t</mi><mi mathvariant="normal">.</mi><mspace width="2em"></mspace><mi mathvariant="normal">&#x2223;</mi><mi mathvariant="normal">&#x2223;</mi><msub><mi>b</mi><mi>j</mi></msub><mi mathvariant="normal">&#x2223;</mi><msub><mi mathvariant="normal">&#x2223;</mi><mn>2</mn></msub><mo>&#x2264;</mo><mn>1</mn><mo separator="true">,</mo><mspace width="1em"></mspace><mi mathvariant="normal">&#x2200;</mi><mi>j</mi><mo>&#x2208;</mo><mn>1</mn><mo separator="true">,</mo><mi mathvariant="normal">.</mi><mi mathvariant="normal">.</mi><mi mathvariant="normal">.</mi><mo separator="true">,</mo><mi>s</mi><mi mathvariant="normal">.</mi></mrow></mtd></mtr></mtable></mrow><annotation encoding="application/x-tex">
     \begin{aligned}
     \min\limits_{a,b} \sum\limits_{i}||x_{S_i}-\sum\limits_j{a_{S_i}^jb_j}||_2^2+\beta||a_{S_i}||_1\\
     s.t. \qquad ||b_j||_2 \leq 1,\quad \forall j\in1,...,s.
     \end{aligned}
     </annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height:1.8781744999999999em;"></span><span class="strut bottom" style="height:3.256349em;vertical-align:-1.3781745000000003em;"></span><span class="base textstyle uncramped"><span class="mord"><span class="mtable"><span class="col-align-r"><span class="vlist"><span style="top:-0.9356024999999999em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="mord textstyle uncramped"><span class="mop op-limits"><span class="vlist"><span style="top:0.6521079999999999em;margin-left:0em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle cramped mtight"><span class="mord scriptstyle cramped mtight"><span class="mord mathit mtight">a</span><span class="mpunct mtight">,</span><span class="mord mathit mtight">b</span></span></span></span><span style="top:2.7755575615628914e-17em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span><span class="mop">min</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span><span class="mop op-limits"><span class="vlist"><span style="top:0.877669em;margin-left:0em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle cramped mtight"><span class="mord scriptstyle cramped mtight"><span class="mord mathit mtight">i</span></span></span></span><span style="top:-0.000004999999999977245em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span><span class="mop op-symbol small-op">&#x2211;</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span><span class="mord mathrm">&#x2223;</span><span class="mord mathrm">&#x2223;</span><span class="mord"><span class="mord mathit">x</span><span class="msupsub"><span class="vlist"><span style="top:0.15000000000000002em;margin-right:0.05em;margin-left:0em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle cramped mtight"><span class="mord scriptstyle cramped mtight"><span class="mord mtight"><span class="mord mathit mtight" style="margin-right:0.05764em;">S</span><span class="msupsub"><span class="vlist"><span style="top:0.143em;margin-right:0.07142857142857144em;margin-left:-0.05764em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-scriptstyle scriptscriptstyle cramped mtight"><span class="mord mathit mtight">i</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span></span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span><span class="mbin">&#x2212;</span><span class="mop op-limits"><span class="vlist"><span style="top:0.8776689999999999em;margin-left:0em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle cramped mtight"><span class="mord mathit mtight" style="margin-right:0.05724em;">j</span></span></span><span style="top:-0.000005000000000088267em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span><span class="mop op-symbol small-op">&#x2211;</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span><span class="mord textstyle uncramped"><span class="mord"><span class="mord mathit">a</span><span class="msupsub"><span class="vlist"><span style="top:0.293531em;margin-left:0em;margin-right:0.05em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle cramped mtight"><span class="mord scriptstyle cramped mtight"><span class="mord mtight"><span class="mord mathit mtight" style="margin-right:0.05764em;">S</span><span class="msupsub"><span class="vlist"><span style="top:0.143em;margin-right:0.07142857142857144em;margin-left:-0.05764em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-scriptstyle scriptscriptstyle cramped mtight"><span class="mord mathit mtight">i</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span></span></span></span><span style="top:-0.480908em;margin-right:0.05em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle uncramped mtight"><span class="mord mathit mtight" style="margin-right:0.05724em;">j</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span><span class="mord"><span class="mord mathit">b</span><span class="msupsub"><span class="vlist"><span style="top:0.15em;margin-right:0.05em;margin-left:0em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle cramped mtight"><span class="mord mathit mtight" style="margin-right:0.05724em;">j</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span></span><span class="mord mathrm">&#x2223;</span><span class="mord"><span class="mord mathrm">&#x2223;</span><span class="msupsub"><span class="vlist"><span style="top:0.24810799999999997em;margin-left:0em;margin-right:0.05em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle cramped mtight"><span class="mord mathrm mtight">2</span></span></span><span style="top:-0.363em;margin-right:0.05em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle uncramped mtight"><span class="mord mathrm mtight">2</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span><span class="mbin">+</span><span class="mord mathit" style="margin-right:0.05278em;">&#x3B2;</span><span class="mord mathrm">&#x2223;</span><span class="mord mathrm">&#x2223;</span><span class="mord"><span class="mord mathit">a</span><span class="msupsub"><span class="vlist"><span style="top:0.15000000000000002em;margin-right:0.05em;margin-left:0em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle cramped mtight"><span class="mord scriptstyle cramped mtight"><span class="mord mtight"><span class="mord mathit mtight" style="margin-right:0.05764em;">S</span><span class="msupsub"><span class="vlist"><span style="top:0.143em;margin-right:0.07142857142857144em;margin-left:-0.05764em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-scriptstyle scriptscriptstyle cramped mtight"><span class="mord mathit mtight">i</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span></span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span><span class="mord mathrm">&#x2223;</span><span class="mord"><span class="mord mathrm">&#x2223;</span><span class="msupsub"><span class="vlist"><span style="top:0.15em;margin-right:0.05em;margin-left:0em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle cramped mtight"><span class="mord mathrm mtight">1</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span></span></span><span style="top:1.0181745000000002em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="mord textstyle uncramped"><span class="mord mathit">s</span><span class="mord mathrm">.</span><span class="mord mathit">t</span><span class="mord mathrm">.</span><span class="mord mathrm"><span class="mspace qquad"></span><span class="mord mathrm">&#x2223;</span></span><span class="mord mathrm">&#x2223;</span><span class="mord"><span class="mord mathit">b</span><span class="msupsub"><span class="vlist"><span style="top:0.15em;margin-right:0.05em;margin-left:0em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle cramped mtight"><span class="mord mathit mtight" style="margin-right:0.05724em;">j</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span><span class="mord mathrm">&#x2223;</span><span class="mord"><span class="mord mathrm">&#x2223;</span><span class="msupsub"><span class="vlist"><span style="top:0.15em;margin-right:0.05em;margin-left:0em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle cramped mtight"><span class="mord mathrm mtight">2</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span><span class="mrel">&#x2264;</span><span class="mord mathrm">1</span><span class="mpunct">,</span><span class="mord mathrm"><span class="mspace quad"></span><span class="mord mathrm">&#x2200;</span></span><span class="mord mathit" style="margin-right:0.05724em;">j</span><span class="mrel">&#x2208;</span><span class="mord mathrm">1</span><span class="mpunct">,</span><span class="mord mathrm">.</span><span class="mord mathrm">.</span><span class="mord mathrm">.</span><span class="mpunct">,</span><span class="mord mathit">s</span><span class="mord mathrm">.</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span></span></span></span></span></p>
<blockquote>
<p><span class="katex"><span class="katex-mathml"><math><semantics><mrow><msubsup><mi>a</mi><mrow><msub><mi>S</mi><mi>i</mi></msub></mrow><mi>j</mi></msubsup></mrow><annotation encoding="application/x-tex">a_{S_i}^j</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height:0.942572em;"></span><span class="strut bottom" style="height:1.3362029999999998em;vertical-align:-0.39363099999999995em;"></span><span class="base textstyle uncramped"><span class="mord"><span class="mord mathit">a</span><span class="msupsub"><span class="vlist"><span style="top:0.293531em;margin-left:0em;margin-right:0.05em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle cramped mtight"><span class="mord scriptstyle cramped mtight"><span class="mord mtight"><span class="mord mathit mtight" style="margin-right:0.05764em;">S</span><span class="msupsub"><span class="vlist"><span style="top:0.143em;margin-right:0.07142857142857144em;margin-left:-0.05764em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-scriptstyle scriptscriptstyle cramped mtight"><span class="mord mathit mtight">i</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span></span></span></span><span style="top:-0.480908em;margin-right:0.05em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle uncramped mtight"><span class="mord mathit mtight" style="margin-right:0.05724em;">j</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span></span></span></span>&#x662F;&#x8F93;&#x5165;<span class="katex"><span class="katex-mathml"><math><semantics><mrow><msub><mi>x</mi><mrow><msub><mi>S</mi><mi>i</mi></msub></mrow></msub></mrow><annotation encoding="application/x-tex">x_{S_i}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height:0.43056em;"></span><span class="strut bottom" style="height:0.68066em;vertical-align:-0.2501em;"></span><span class="base textstyle uncramped"><span class="mord"><span class="mord mathit">x</span><span class="msupsub"><span class="vlist"><span style="top:0.15000000000000002em;margin-right:0.05em;margin-left:0em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle cramped mtight"><span class="mord scriptstyle cramped mtight"><span class="mord mtight"><span class="mord mathit mtight" style="margin-right:0.05764em;">S</span><span class="msupsub"><span class="vlist"><span style="top:0.143em;margin-right:0.07142857142857144em;margin-left:-0.05764em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-scriptstyle scriptscriptstyle cramped mtight"><span class="mord mathit mtight">i</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span></span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span></span></span></span>&#x5728;&#x65B0;&#x7684;&#x57FA;<span class="katex"><span class="katex-mathml"><math><semantics><mrow><msub><mi>b</mi><mi>j</mi></msub></mrow><annotation encoding="application/x-tex">b_j</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height:0.69444em;"></span><span class="strut bottom" style="height:0.980548em;vertical-align:-0.286108em;"></span><span class="base textstyle uncramped"><span class="mord"><span class="mord mathit">b</span><span class="msupsub"><span class="vlist"><span style="top:0.15em;margin-right:0.05em;margin-left:0em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle cramped mtight"><span class="mord mathit mtight" style="margin-right:0.05724em;">j</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span></span></span></span>&#x4E0B;&#x7684;&#x8868;&#x793A;&#xFF0C;<span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>&#x3B2;</mi></mrow><annotation encoding="application/x-tex">\beta</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height:0.69444em;"></span><span class="strut bottom" style="height:0.8888799999999999em;vertical-align:-0.19444em;"></span><span class="base textstyle uncramped"><span class="mord mathit" style="margin-right:0.05278em;">&#x3B2;</span></span></span></span>&#x662F;&#x5E73;&#x8861;&#x4E86;&#x7279;&#x5F81;&#x6784;&#x9020;&#x9879;&#x548C;&#x6B63;&#x5219;&#x5316;&#x9879;&#x7684;&#x7CFB;&#x6570;.</p>
</blockquote>
</li>
<li><p>&#x5B66;&#x4E60;&#x5B8C;&#x57FA;&#x5411;&#x91CF; <span class="katex"><span class="katex-mathml"><math><semantics><mrow><msub><mi>b</mi><mi>i</mi></msub></mrow><annotation encoding="application/x-tex">b_i</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height:0.69444em;"></span><span class="strut bottom" style="height:0.84444em;vertical-align:-0.15em;"></span><span class="base textstyle uncramped"><span class="mord"><span class="mord mathit">b</span><span class="msupsub"><span class="vlist"><span style="top:0.15em;margin-right:0.05em;margin-left:0em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle cramped mtight"><span class="mord mathit mtight">i</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span></span></span></span> &#x540E;&#xFF0C;&#x5C31;&#x53EF;&#x4EE5;&#x5BF9;&#x76EE;&#x6807;&#x6570;&#x636E;&#x5E94;&#x7528;&#x4E0B;&#x5217;&#x4F18;&#x5316;&#x7B97;&#x6CD5;&#xFF0C;&#x8BA9; <span class="katex"><span class="katex-mathml"><math><semantics><mrow><msub><mi>b</mi><mi>i</mi></msub></mrow><annotation encoding="application/x-tex">b_i</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height:0.69444em;"></span><span class="strut bottom" style="height:0.84444em;vertical-align:-0.15em;"></span><span class="base textstyle uncramped"><span class="mord"><span class="mord mathit">b</span><span class="msupsub"><span class="vlist"><span style="top:0.15em;margin-right:0.05em;margin-left:0em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle cramped mtight"><span class="mord mathit mtight">i</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span></span></span></span> &#x5B66;&#x4E60;&#x5230;&#x66F4;&#x9AD8;&#x7EA7;&#x522B;&#x7684;&#x7279;&#x5F81;
<span class="katex"><span class="katex-mathml"><math><semantics><mrow><msubsup><mi>a</mi><mrow><msub><mi>T</mi><mi>i</mi></msub></mrow><mo>&#x2217;</mo></msubsup><mo>=</mo><mi>arg</mi><msub><mi>min</mi><mrow><msub><mi>a</mi><mrow><msub><mi>T</mi><mi>i</mi></msub></mrow></msub></mrow></msub><mo>&#x2225;</mo><msub><mi>x</mi><mrow><msub><mi>T</mi><mi>i</mi></msub></mrow></msub><mo>&#x2212;</mo><msub><mo>&#x2211;</mo><mi>j</mi></msub><msubsup><mi>a</mi><mrow><msub><mi>T</mi><mi>i</mi></msub></mrow><mi>j</mi></msubsup><msub><mi>b</mi><mi>j</mi></msub><msubsup><mo>&#x2225;</mo><mn>2</mn><mn>2</mn></msubsup><mo>+</mo><mi>&#x3B2;</mi><mi mathvariant="normal">&#x2225;</mi><msub><mi>a</mi><mrow><msub><mi>T</mi><mi>i</mi></msub></mrow></msub><msub><mi mathvariant="normal">&#x2225;</mi><mn>1</mn></msub><mi mathvariant="normal">.</mi></mrow><annotation encoding="application/x-tex">
     a_{T_i}^*=\arg \min\limits_{a_{T_i}}\lVert x_{T_i}-\sum\limits_ja_{T_i}^jb_j\rVert_2^2+\beta\|a_{T_i}\|_1.
     </annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height:0.942572em;"></span><span class="strut bottom" style="height:2.056349em;vertical-align:-1.113777em;"></span><span class="base textstyle uncramped"><span class="mord"><span class="mord mathit">a</span><span class="msupsub"><span class="vlist"><span style="top:0.251027em;margin-left:0em;margin-right:0.05em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle cramped mtight"><span class="mord scriptstyle cramped mtight"><span class="mord mtight"><span class="mord mathit mtight" style="margin-right:0.13889em;">T</span><span class="msupsub"><span class="vlist"><span style="top:0.143em;margin-right:0.07142857142857144em;margin-left:-0.13889em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-scriptstyle scriptscriptstyle cramped mtight"><span class="mord mathit mtight">i</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span></span></span></span><span style="top:-0.363em;margin-right:0.05em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle uncramped mtight"><span class="mbin mtight">&#x2217;</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span><span class="mrel">=</span><span class="mop">ar<span style="margin-right:0.01389em;">g</span></span><span class="mop op-limits"><span class="vlist"><span style="top:0.5999999999999999em;margin-left:0em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle cramped mtight"><span class="mord scriptstyle cramped mtight"><span class="mord mtight"><span class="mord mathit mtight">a</span><span class="msupsub"><span class="vlist"><span style="top:0.14329285714285717em;margin-right:0.07142857142857144em;margin-left:0em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-scriptstyle scriptscriptstyle cramped mtight"><span class="mord scriptscriptstyle cramped mtight"><span class="mord mtight"><span class="mord mathit mtight" style="margin-right:0.13889em;">T</span><span class="msupsub"><span class="vlist"><span style="top:0.31472em;margin-right:0.1em;margin-left:-0.13889em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-scriptscriptstyle scriptscriptstyle cramped mtight"><span class="mord mathit mtight">i</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span></span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span></span></span></span><span style="top:0em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span><span class="mop">min</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span><span class="mopen">&#x2225;</span><span class="mord"><span class="mord mathit">x</span><span class="msupsub"><span class="vlist"><span style="top:0.15000000000000002em;margin-right:0.05em;margin-left:0em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle cramped mtight"><span class="mord scriptstyle cramped mtight"><span class="mord mtight"><span class="mord mathit mtight" style="margin-right:0.13889em;">T</span><span class="msupsub"><span class="vlist"><span style="top:0.143em;margin-right:0.07142857142857144em;margin-left:-0.13889em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-scriptstyle scriptscriptstyle cramped mtight"><span class="mord mathit mtight">i</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span></span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span><span class="mbin">&#x2212;</span><span class="mop op-limits"><span class="vlist"><span style="top:0.8776689999999999em;margin-left:0em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle cramped mtight"><span class="mord mathit mtight" style="margin-right:0.05724em;">j</span></span></span><span style="top:-0.000005000000000088267em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span><span class="mop op-symbol small-op">&#x2211;</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span><span class="mord"><span class="mord mathit">a</span><span class="msupsub"><span class="vlist"><span style="top:0.293531em;margin-left:0em;margin-right:0.05em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle cramped mtight"><span class="mord scriptstyle cramped mtight"><span class="mord mtight"><span class="mord mathit mtight" style="margin-right:0.13889em;">T</span><span class="msupsub"><span class="vlist"><span style="top:0.143em;margin-right:0.07142857142857144em;margin-left:-0.13889em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-scriptstyle scriptscriptstyle cramped mtight"><span class="mord mathit mtight">i</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span></span></span></span><span style="top:-0.480908em;margin-right:0.05em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle uncramped mtight"><span class="mord mathit mtight" style="margin-right:0.05724em;">j</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span><span class="mord"><span class="mord mathit">b</span><span class="msupsub"><span class="vlist"><span style="top:0.15em;margin-right:0.05em;margin-left:0em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle cramped mtight"><span class="mord mathit mtight" style="margin-right:0.05724em;">j</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span><span class="mclose"><span class="mclose">&#x2225;</span><span class="msupsub"><span class="vlist"><span style="top:0.24810799999999997em;margin-left:0em;margin-right:0.05em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle cramped mtight"><span class="mord mathrm mtight">2</span></span></span><span style="top:-0.363em;margin-right:0.05em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle uncramped mtight"><span class="mord mathrm mtight">2</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span><span class="mbin">+</span><span class="mord mathit" style="margin-right:0.05278em;">&#x3B2;</span><span class="mord mathrm">&#x2225;</span><span class="mord"><span class="mord mathit">a</span><span class="msupsub"><span class="vlist"><span style="top:0.15000000000000002em;margin-right:0.05em;margin-left:0em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle cramped mtight"><span class="mord scriptstyle cramped mtight"><span class="mord mtight"><span class="mord mathit mtight" style="margin-right:0.13889em;">T</span><span class="msupsub"><span class="vlist"><span style="top:0.143em;margin-right:0.07142857142857144em;margin-left:-0.13889em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-scriptstyle scriptscriptstyle cramped mtight"><span class="mord mathit mtight">i</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span></span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span><span class="mord"><span class="mord mathrm">&#x2225;</span><span class="msupsub"><span class="vlist"><span style="top:0.15em;margin-right:0.05em;margin-left:0em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle cramped mtight"><span class="mord mathrm mtight">1</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span><span class="mord mathrm">.</span></span></span></span></p>
</li>
<li><p>&#x6700;&#x540E;&#xFF0C;&#x9274;&#x522B;&#x7B97;&#x6CD5;&#x5C31;&#x53EF;&#x4EE5;&#x5E94;&#x7528;&#x5230;&#x5177;&#x6709;&#x76F8;&#x5E94;&#x6807;&#x7B7E;&#x7684;<span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo>{</mo><msubsup><mi>a</mi><mrow><msub><mi>T</mi><mi>i</mi></msub></mrow><mo>&#x2217;</mo></msubsup><msup><mo>}</mo><mrow><msup><mrow></mrow><mrow><mi mathvariant="normal">&#x2032;</mi></mrow></msup></mrow></msup></mrow><annotation encoding="application/x-tex">\{a_{T_i}^*\}^{&apos;}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height:0.94248em;"></span><span class="strut bottom" style="height:1.293607em;vertical-align:-0.35112699999999997em;"></span><span class="base textstyle uncramped"><span class="mopen">{</span><span class="mord"><span class="mord mathit">a</span><span class="msupsub"><span class="vlist"><span style="top:0.251027em;margin-left:0em;margin-right:0.05em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle cramped mtight"><span class="mord scriptstyle cramped mtight"><span class="mord mtight"><span class="mord mathit mtight" style="margin-right:0.13889em;">T</span><span class="msupsub"><span class="vlist"><span style="top:0.143em;margin-right:0.07142857142857144em;margin-left:-0.13889em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-scriptstyle scriptscriptstyle cramped mtight"><span class="mord mathit mtight">i</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span></span></span></span><span style="top:-0.363em;margin-right:0.05em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle uncramped mtight"><span class="mbin mtight">&#x2217;</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span><span class="mclose"><span class="mclose">}</span><span class="msupsub"><span class="vlist"><span style="top:-0.363em;margin-right:0.05em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle uncramped mtight"><span class="mord scriptstyle uncramped mtight"><span class="mord mtight"><span></span><span class="msupsub"><span class="vlist"><span style="top:-0.431em;margin-right:0.07142857142857144em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-scriptstyle scriptscriptstyle uncramped mtight"><span class="mord scriptscriptstyle uncramped mtight"><span class="mord mathrm mtight">&#x2032;</span></span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span></span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span></span></span></span>,&#x7528;&#x6765;&#x8BAD;&#x7EC3;&#x5206;&#x7C7B;&#x6216;&#x6216;&#x56DE;&#x5F52;&#x6A21;&#x578B;&#x7528;&#x4E8E;&#x76EE;&#x6807;&#x57DF;&#xFF0C;&#x4F46;&#x5728;&#x6E90;&#x57DF;&#x4E0A;&#x8BAD;&#x7EC3;&#x51FA;&#x7684;&#x57FA;&#x5411;&#x91CF;&#x53EF;&#x80FD;&#x5E76;&#x4E0D;&#x9002;&#x5408;&#x5728;&#x76EE;&#x6807;&#x57DF;&#x4E2D;&#x4F7F;&#x7528;</p>
</li>
</ol>
</li>
<li><p>&#x6709;&#x4EBA;&#x63D0;&#x51FA;&#x4E86;&#x4E00;&#x79CD;&#x57FA;&#x4E8E;&#x666E;&#x7F57;&#x79D1;&#x65AF;&#x7279;&#x65AF;&#x5206;&#x6790;&#x7684;&#x6D41;&#x5F62;&#x5BF9;&#x9F50;&#x65B9;&#x6CD5;&#x3002;&#x901A;&#x8FC7;&#x5BF9;&#x9F50;&#x7684;&#x6D41;&#x5F62;&#x8FDB;&#x884C;&#x77E5;&#x8BC6;&#x7684;&#x8DE8;&#x57DF;&#x4F20;&#x9012;</p>
</li>
</ul>
<h3 id="&#x4F20;&#x9012;&#x53C2;&#x6570;&#x77E5;&#x8BC6;"><a name="&#x4F20;&#x9012;&#x53C2;&#x6570;&#x77E5;&#x8BC6;" class="anchor-navigation-ex-anchor" href="#&#x4F20;&#x9012;&#x53C2;&#x6570;&#x77E5;&#x8BC6;"><i class="fa fa-link" aria-hidden="true"></i></a>1.3.3. &#x4F20;&#x9012;&#x53C2;&#x6570;&#x77E5;&#x8BC6;</h3>
<ul>
<li>&#x672C;&#x8282;&#x63CF;&#x8FF0;&#x7684;&#x65B9;&#x6CD5;&#x591A;&#x4E3A;&#x591A;&#x4EFB;&#x52A1;&#x800C;&#x8BBE;&#x8BA1;&#x7684;&#xFF0C;&#x5B83;&#x4E5F;&#x5BB9;&#x6613;&#x88AB;&#x4FEE;&#x6539;&#x5230;&#x5E94;&#x7528;&#x81F3;&#x8FC1;&#x79FB;&#x5B66;&#x4E60;&#x3002;&#x6211;&#x4EEC;&#x5E94;&#x5F53;&#x5728;&#x76EE;&#x6807;&#x57DF;&#x4E0A;&#x7684;&#x635F;&#x5931;&#x51FD;&#x6570;&#x5206;&#x914D;&#x66F4;&#x5927;&#x7684;&#x6743;&#x91CD;</li>
</ul>
<h3 id="&#x4F20;&#x9012;&#x5173;&#x7CFB;&#x77E5;&#x8BC6;"><a name="&#x4F20;&#x9012;&#x5173;&#x7CFB;&#x77E5;&#x8BC6;" class="anchor-navigation-ex-anchor" href="#&#x4F20;&#x9012;&#x5173;&#x7CFB;&#x77E5;&#x8BC6;"><i class="fa fa-link" aria-hidden="true"></i></a>1.3.4. &#x4F20;&#x9012;&#x5173;&#x7CFB;&#x77E5;&#x8BC6;</h3>
<p><code>i.i.d: &#x72EC;&#x7ACB;&#x540C;&#x5206;&#x5E03;</code></p>
<blockquote>
<p>&#x5B83;&#x8BD5;&#x56FE;&#x5C06;&#x6570;&#x636E;&#x4E4B;&#x95F4;&#x7684;&#x5173;&#x7CFB;&#x4ECE;&#x6E90;&#x57DF;&#x8F6C;&#x79FB;&#x5230;&#x76EE;&#x6807;&#x57DF;&#x3002;</p>
</blockquote>
<ul>
<li>TAMAR&#x7B97;&#x6CD5;&#xFF1A;&#x5229;&#x7528;&#x9A6C;&#x5C14;&#x79D1;&#x592B;&#x903B;&#x8F91;&#x7F51;&#x7EDC;&#x5728;&#x5173;&#x7CFB;&#x57DF;&#x4E2D;&#x4F20;&#x9012;&#x5173;&#x7CFB;&#x77E5;&#x8BC6;&#x3002;<ul>
<li>&#x57FA;&#x7840;&#xFF1A;&#x5982;&#x679C;&#x4E24;&#x4E2A;&#x57DF;&#x9879;&#x76EE;&#x5173;&#x8054;&#xFF0C;&#x5219;&#x53EF;&#x80FD;&#x5B58;&#x5728;&#x4ECE;&#x6E90;&#x57DF;&#x5230;&#x76EE;&#x6807;&#x57DF;&#x8FDE;&#x63A5;&#x5B9E;&#x4F53;&#x53CA;&#x5176;&#x5173;&#x7CFB;&#x7684;&#x6620;&#x5C04;</li>
<li>&#x4E24;&#x4E2A;&#x9636;&#x6BB5;<ul>
<li>&#x57FA;&#x4E8E;&#x52A0;&#x6743;&#x4F2A;&#x5BF9;&#x6570;&#x4F3C;&#x7136;&#x5EA6;&#x91CF;&#xFF08;WPLL&#xFF09;&#xFF0C;&#x6784;&#x5EFA;&#x4ECE;&#x6E90;&#x57DF;&#x5230;&#x76EE;&#x6807;&#x57DF;&#x7684;&#x6620;&#x5C04;</li>
<li>&#x901A;&#x8FC7;FORTE&#x7B97;&#x6CD5;(&#x7528;&#x4E8E;&#x4FEE;&#x6539;&#x4E00;&#x9636;&#x7406;&#x8BBA;&#x7684;&#x9B3C;&#x9A6C;&#x903B;&#x8F91;&#x7F16;&#x7A0B;&#xFF08;ILP&#xFF09;suanfa )&#x5BF9;&#x76EE;&#x6807;&#x57DF;&#x4E2D;&#x7684;&#x6620;&#x5C04;&#x7ED3;&#x6784;&#x8FDB;&#x884C;&#x4FEE;&#x6539;</li>
</ul>
</li>
</ul>
</li>
</ul>
<h2 id="&#x8F6C;&#x5BFC;&#x8FC1;&#x79FB;&#x5B66;&#x4E60;"><a name="&#x8F6C;&#x5BFC;&#x8FC1;&#x79FB;&#x5B66;&#x4E60;" class="anchor-navigation-ex-anchor" href="#&#x8F6C;&#x5BFC;&#x8FC1;&#x79FB;&#x5B66;&#x4E60;"><i class="fa fa-link" aria-hidden="true"></i></a>1.4. &#x8F6C;&#x5BFC;&#x8FC1;&#x79FB;&#x5B66;&#x4E60;</h2>
<p>&#x8981;&#x6C42;&#x6E90;&#x4EFB;&#x52A1;&#x548C;&#x76EE;&#x6807;&#x4EFB;&#x52A1;&#x76F8;&#x540C;&#xFF0C;&#x5C3D;&#x7BA1;&#x57DF;&#x53EF;&#x80FD;&#x4E0D;&#x540C;&#x3002;&#x8FDB;&#x4E00;&#x6B65;&#x8981;&#x6C42;&#x672A;&#x6807;&#x8BB0;&#x6570;&#x636E;&#x4E5F;&#x662F;&#x53EF;&#x7528;&#x7684;&#x3002;</p>
<p>&#x8F6C;&#x5BFC;&#x6709;&#x51E0;&#x79CD;&#x542B;&#x4E49;&#xFF1A;</p>
<ul>
<li>&#x5728;&#x4F20;&#x7EDF;&#x673A;&#x5668;&#x5B66;&#x4E60;&#x4E2D;&#xFF0C;&#x5B83;&#x8981;&#x6C42;&#x5728;&#x8BAD;&#x7EC3;&#x65F6;&#x770B;&#x5230;&#x6240;&#x6709;&#x6D4B;&#x8BD5;&#x6570;&#x636E;&#xFF0C;&#x4E14;&#x5B66;&#x4E60;&#x5230;&#x7684;&#x6A21;&#x578B;&#x4E0D;&#x80FD;&#x88AB;&#x7528;&#x4E0E;&#x672A;&#x6765;&#x7684;&#x6570;&#x636E;&#x3002;</li>
<li>&#x5728;&#x8FC1;&#x79FB;&#x5B66;&#x4E60;&#x7684;&#x5206;&#x7C7B;&#x4E2D;&#xFF0C;&#x7528;&#x6765;&#x5F3A;&#x8C03;&#x4EFB;&#x52A1;&#x5FC5;&#x987B;&#x76F8;&#x540C;&#xFF0C;&#x4E14;&#x5728;&#x76EE;&#x6807;&#x57DF;&#x4E2D;&#x5FC5;&#x987B;&#x6709;&#x4E00;&#x4E9B;&#x672A;&#x6807;&#x8BB0;&#x7684;&#x6570;&#x636E;&#x53EF;&#x7528;</li>
</ul>
<p><strong>&#x5B9A;&#x4E49;3(&#x8F6C;&#x5BFC;&#x8FC1;&#x79FB;&#x5B66;&#x4E60;)</strong>&#xFF1A;&#x7ED9;&#x5B9A;<span class="katex"><span class="katex-mathml"><math><semantics><mrow><msub><mi>D</mi><mi>S</mi></msub><mo separator="true">,</mo><msub><mi>T</mi><mi>S</mi></msub><mo separator="true">,</mo><msub><mi>D</mi><mi>T</mi></msub><mo separator="true">,</mo><msub><mi>T</mi><mi>T</mi></msub></mrow><annotation encoding="application/x-tex">D_S,T_S,D_T,T_T</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height:0.68333em;"></span><span class="strut bottom" style="height:0.8777699999999999em;vertical-align:-0.19444em;"></span><span class="base textstyle uncramped"><span class="mord"><span class="mord mathit" style="margin-right:0.02778em;">D</span><span class="msupsub"><span class="vlist"><span style="top:0.15em;margin-right:0.05em;margin-left:-0.02778em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle cramped mtight"><span class="mord mathit mtight" style="margin-right:0.05764em;">S</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span><span class="mpunct">,</span><span class="mord"><span class="mord mathit" style="margin-right:0.13889em;">T</span><span class="msupsub"><span class="vlist"><span style="top:0.15em;margin-right:0.05em;margin-left:-0.13889em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle cramped mtight"><span class="mord mathit mtight" style="margin-right:0.05764em;">S</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span><span class="mpunct">,</span><span class="mord"><span class="mord mathit" style="margin-right:0.02778em;">D</span><span class="msupsub"><span class="vlist"><span style="top:0.15em;margin-right:0.05em;margin-left:-0.02778em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle cramped mtight"><span class="mord mathit mtight" style="margin-right:0.13889em;">T</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span><span class="mpunct">,</span><span class="mord"><span class="mord mathit" style="margin-right:0.13889em;">T</span><span class="msupsub"><span class="vlist"><span style="top:0.15em;margin-right:0.05em;margin-left:-0.13889em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle cramped mtight"><span class="mord mathit mtight" style="margin-right:0.13889em;">T</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span></span></span></span>&#xFF0C;&#x5B83;&#x65E8;&#x5728;&#x4F7F;&#x7528;&#x6E90;&#x57DF;&#x4E0A;&#x7684;&#x6570;&#x636E;&#x63D0;&#x9AD8;&#x5728;&#x76EE;&#x6807;&#x57DF;&#x4E0A;&#x7684;&#x9884;&#x6D4B;&#x51FD;&#x6570;&#x3002;&#x6B64;&#x5916;&#xFF0C;&#x4E00;&#x4E9B;&#x672A;&#x6807;&#x8BB0;&#x7684;&#x6570;&#x636E;&#x4E5F;&#x9700;&#x8981;&#x88AB;&#x7528;&#x5230;&#x3002;</p>
<p>&#x8F6C;&#x5BFC;&#x8FC1;&#x79FB;&#x5B66;&#x4E60;&#x4E3B;&#x8981;&#x6709;&#x4E24;&#x79CD;&#x60C5;&#x51B5;&#xFF1A;1&#xFF09;&#x6E90;&#x57DF;&#x548C;&#x76EE;&#x6807;&#x57DF;&#x4E4B;&#x95F4;&#x7684;&#x7279;&#x5F81;&#x7A7A;&#x95F4;&#x4E0D;&#x540C;&#xFF1B;2&#xFF09;&#x57DF;&#x4E4B;&#x95F4;&#x7684;&#x7279;&#x5F81;&#x7A7A;&#x95F4;&#x76F8;&#x540C;&#xFF0C;&#x4F46;&#x8F93;&#x5165;&#x6570;&#x636E;&#x7684;&#x8FB9;&#x7F18;&#x5206;&#x5E03;&#x6982;&#x7387;&#x51FD;&#x6570;&#x4E0D;&#x540C;</p>
<h3 id="&#x5B9E;&#x4F8B;&#x77E5;&#x8BC6;&#x7684;&#x8F6C;&#x79FB;"><a name="&#x5B9E;&#x4F8B;&#x77E5;&#x8BC6;&#x7684;&#x8F6C;&#x79FB;" class="anchor-navigation-ex-anchor" href="#&#x5B9E;&#x4F8B;&#x77E5;&#x8BC6;&#x7684;&#x8F6C;&#x79FB;"><i class="fa fa-link" aria-hidden="true"></i></a>1.4.1. &#x5B9E;&#x4F8B;&#x77E5;&#x8BC6;&#x7684;&#x8F6C;&#x79FB;</h3>
<blockquote>
<p>&#x673A;&#x5668;&#x5B66;&#x4E60;&#x7406;&#x8BBA; &#x4E4B; &#x7ECF;&#x9A8C;&#x98CE;&#x9669;&#x6700;&#x5C0F;&#x5316;&#xFF08;Empirical Risk Minimization&#xFF09;</p>
</blockquote>
<h3 id="&#x4F20;&#x9012;&#x7279;&#x5F81;&#x8868;&#x793A;&#x7684;&#x77E5;&#x8BC6;_1"><a name="&#x4F20;&#x9012;&#x7279;&#x5F81;&#x8868;&#x793A;&#x7684;&#x77E5;&#x8BC6;_1" class="anchor-navigation-ex-anchor" href="#&#x4F20;&#x9012;&#x7279;&#x5F81;&#x8868;&#x793A;&#x7684;&#x77E5;&#x8BC6;_1"><i class="fa fa-link" aria-hidden="true"></i></a>1.4.2. &#x4F20;&#x9012;&#x7279;&#x5F81;&#x8868;&#x793A;&#x7684;&#x77E5;&#x8BC6;</h3>
<ul>
<li><code>Blitzer</code>&#x7B49;&#x4EBA;&#x63D0;&#x51FA;&#x4E86;&#x4E00;&#x79CD;&#x7ED3;&#x6784;&#x5BF9;&#x5E94;&#x5B66;&#x4E60;&#xFF08;SCL&#xFF09;&#x7B97;&#x6CD5;&#xFF0C;&#x5229;&#x7528;&#x76EE;&#x6807;&#x57DF;&#x4E2D;&#x7684;&#x672A;&#x6807;&#x8BB0;&#x6570;&#x636E;&#x63D0;&#x53D6;&#x51FA;&#x4E00;&#x4E9B;&#x5173;&#x952E;&#x7279;&#x5F81;&#xFF0C;&#x4EE5;&#x51CF;&#x5C0F;&#x57DF;&#x4E4B;&#x95F4;&#x7684;&#x5DEE;&#x5F02;&#x3002;<ul>
<li>&#x7B2C;&#x4E00;&#x6B65;&#x662F;&#x5728;&#x6765;&#x81EA;&#x4E24;&#x4E2A;&#x57DF;&#x7684;&#x672A;&#x6807;&#x8BB0;&#x6570;&#x636E;&#x4E0A;&#x5B9A;&#x4E49;&#x4E00;&#x7EC4;&#x4E2D;&#x67A2;&#x7279;&#x5F81;&#xFF08;&#x5171;m&#x4E2A;&#xFF09;</li>
<li>&#x4ECE;&#x6570;&#x636E;&#x4E2D;&#x79FB;&#x9664;&#x4E86;&#x8FD9;&#x4E9B;&#x67A2;&#x8F74;&#x7279;&#x5F81;&#x540E;&#xFF0C;&#x5C06;&#x6BCF;&#x4E2A;&#x67A2;&#x8F74;&#x89C6;&#x4E3A;&#x65B0;&#x7684;&#x6807;&#x7B7E;&#x5411;&#x91CF;&#xFF0C;&#x53EF;&#x4EE5;&#x6784;&#x9020;m&#x5206;&#x7C7B;&#x95EE;&#x9898;&#xFF0C;&#x5982;&#x4E0B;&#x6240;&#x793A;
<span class="katex"><span class="katex-mathml"><math><semantics><mrow><msub><mi>f</mi><mi>l</mi></msub><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mi>s</mi><mi>g</mi><mi>n</mi><mo>(</mo><msubsup><mi>w</mi><mi>l</mi><mi>T</mi></msubsup><mo>&#x22C5;</mo><mi>x</mi><mo>)</mo><mo separator="true">,</mo><mspace width="1em"></mspace><mi>l</mi><mo>=</mo><mn>1</mn><mo separator="true">,</mo><mi mathvariant="normal">.</mi><mi mathvariant="normal">.</mi><mi mathvariant="normal">.</mi><mo separator="true">,</mo><mi>m</mi><mi mathvariant="normal">.</mi></mrow><annotation encoding="application/x-tex">f_l(x)=sgn(w_l^T \cdot x),\quad l=1,...,m.</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height:0.8413309999999999em;"></span><span class="strut bottom" style="height:1.1244389999999997em;vertical-align:-0.2831079999999999em;"></span><span class="base textstyle uncramped"><span class="mord"><span class="mord mathit" style="margin-right:0.10764em;">f</span><span class="msupsub"><span class="vlist"><span style="top:0.15em;margin-right:0.05em;margin-left:-0.10764em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle cramped mtight"><span class="mord mathit mtight" style="margin-right:0.01968em;">l</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span><span class="mopen">(</span><span class="mord mathit">x</span><span class="mclose">)</span><span class="mrel">=</span><span class="mord mathit">s</span><span class="mord mathit" style="margin-right:0.03588em;">g</span><span class="mord mathit">n</span><span class="mopen">(</span><span class="mord"><span class="mord mathit" style="margin-right:0.02691em;">w</span><span class="msupsub"><span class="vlist"><span style="top:0.2831079999999999em;margin-left:-0.02691em;margin-right:0.05em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle cramped mtight"><span class="mord mathit mtight" style="margin-right:0.01968em;">l</span></span></span><span style="top:-0.363em;margin-right:0.05em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle uncramped mtight"><span class="mord mathit mtight" style="margin-right:0.13889em;">T</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span><span class="mbin">&#x22C5;</span><span class="mord mathit">x</span><span class="mclose">)</span><span class="mpunct">,</span><span class="mord mathit"><span class="mspace quad"></span><span class="mord mathit" style="margin-right:0.01968em;">l</span></span><span class="mrel">=</span><span class="mord mathrm">1</span><span class="mpunct">,</span><span class="mord mathrm">.</span><span class="mord mathrm">.</span><span class="mord mathrm">.</span><span class="mpunct">,</span><span class="mord mathit">m</span><span class="mord mathrm">.</span></span></span></span>
SCI&#x53EF;&#x4EE5;&#x5B66;&#x4E60;&#x77E9;&#x9635;<span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>W</mi><mo>=</mo><mo>[</mo><msub><mi>w</mi><mn>1</mn></msub><msub><mi>w</mi><mn>2</mn></msub><mi mathvariant="normal">.</mi><mi mathvariant="normal">.</mi><mi mathvariant="normal">.</mi><msub><mi>w</mi><mi>m</mi></msub><mo>]</mo></mrow><annotation encoding="application/x-tex">W=[w_1 w_2...w_m]</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height:0.75em;"></span><span class="strut bottom" style="height:1em;vertical-align:-0.25em;"></span><span class="base textstyle uncramped"><span class="mord mathit" style="margin-right:0.13889em;">W</span><span class="mrel">=</span><span class="mopen">[</span><span class="mord"><span class="mord mathit" style="margin-right:0.02691em;">w</span><span class="msupsub"><span class="vlist"><span style="top:0.15em;margin-right:0.05em;margin-left:-0.02691em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle cramped mtight"><span class="mord mathrm mtight">1</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span><span class="mord"><span class="mord mathit" style="margin-right:0.02691em;">w</span><span class="msupsub"><span class="vlist"><span style="top:0.15em;margin-right:0.05em;margin-left:-0.02691em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle cramped mtight"><span class="mord mathrm mtight">2</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span><span class="mord mathrm">.</span><span class="mord mathrm">.</span><span class="mord mathrm">.</span><span class="mord"><span class="mord mathit" style="margin-right:0.02691em;">w</span><span class="msupsub"><span class="vlist"><span style="top:0.15em;margin-right:0.05em;margin-left:-0.02691em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle cramped mtight"><span class="mord mathit mtight">m</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span><span class="mclose">]</span></span></span></span>&#x4E2D;&#x7684;&#x53C2;&#x6570;</li>
<li>&#x5C06;&#x5947;&#x5F02;&#x503C;&#x5206;&#x89E3;&#x5E94;&#x7528;&#x4E8E;&#x77E9;&#x9635;W</li>
</ul>
</li>
<li>SCL&#x53EF;&#x4EE5;&#x51CF;&#x5C11;&#x57DF;&#x4E4B;&#x95F4;&#x7684;&#x5DEE;&#x5F02;&#xFF0C;&#x4F46;&#x5982;&#x4F55;&#x9009;&#x62E9;&#x4E2D;&#x67A2;&#x7279;&#x5F81;&#x662F;&#x56F0;&#x96BE;&#x7684;&#xFF0C;&#x5E76;&#x53D6;&#x51B3;&#x4E8E;&#x9886;&#x57DF;</li>
<li>&#x5EFA;&#x8BAE;&#x4F7F;&#x7528;&#x4E92;&#x4FE1;&#x606F;&#x6765;&#x9009;&#x62E9;&#x67A2;&#x8F74;&#x7279;&#x5F81;&#xFF0C;&#x800C;&#x4E0D;&#x662F;&#x4F7F;&#x7528;&#x66F4;&#x591A;&#x7684;&#x542F;&#x53D1;&#x5F0F;&#x6807;&#x51C6;</li>
</ul>
<h2 id="&#x65E0;&#x76D1;&#x7763;&#x8FC1;&#x79FB;&#x5B66;&#x4E60;"><a name="&#x65E0;&#x76D1;&#x7763;&#x8FC1;&#x79FB;&#x5B66;&#x4E60;" class="anchor-navigation-ex-anchor" href="#&#x65E0;&#x76D1;&#x7763;&#x8FC1;&#x79FB;&#x5B66;&#x4E60;"><i class="fa fa-link" aria-hidden="true"></i></a>1.5. &#x65E0;&#x76D1;&#x7763;&#x8FC1;&#x79FB;&#x5B66;&#x4E60;</h2>
<p><strong>&#x5B9A;&#x4E49;4(&#x65E0;&#x76D1;&#x7763;&#x8FC1;&#x79FB;&#x5B66;&#x4E60;)</strong>&#xFF1A;&#x7ED9;&#x5B9A;<span class="katex"><span class="katex-mathml"><math><semantics><mrow><msub><mi>T</mi><mi>S</mi></msub><mo separator="true">,</mo><msub><mi>D</mi><mi>S</mi></msub><mo separator="true">,</mo><msub><mi>D</mi><mi>T</mi></msub><mo separator="true">,</mo><msub><mi>T</mi><mi>T</mi></msub></mrow><annotation encoding="application/x-tex">T_S,D_S,D_T,T_T</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height:0.68333em;"></span><span class="strut bottom" style="height:0.8777699999999999em;vertical-align:-0.19444em;"></span><span class="base textstyle uncramped"><span class="mord"><span class="mord mathit" style="margin-right:0.13889em;">T</span><span class="msupsub"><span class="vlist"><span style="top:0.15em;margin-right:0.05em;margin-left:-0.13889em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle cramped mtight"><span class="mord mathit mtight" style="margin-right:0.05764em;">S</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span><span class="mpunct">,</span><span class="mord"><span class="mord mathit" style="margin-right:0.02778em;">D</span><span class="msupsub"><span class="vlist"><span style="top:0.15em;margin-right:0.05em;margin-left:-0.02778em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle cramped mtight"><span class="mord mathit mtight" style="margin-right:0.05764em;">S</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span><span class="mpunct">,</span><span class="mord"><span class="mord mathit" style="margin-right:0.02778em;">D</span><span class="msupsub"><span class="vlist"><span style="top:0.15em;margin-right:0.05em;margin-left:-0.02778em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle cramped mtight"><span class="mord mathit mtight" style="margin-right:0.13889em;">T</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span><span class="mpunct">,</span><span class="mord"><span class="mord mathit" style="margin-right:0.13889em;">T</span><span class="msupsub"><span class="vlist"><span style="top:0.15em;margin-right:0.05em;margin-left:-0.13889em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle cramped mtight"><span class="mord mathit mtight" style="margin-right:0.13889em;">T</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span></span></span></span>,&#x5B83;&#x7684;&#x76EE;&#x7684;&#x4E0E;&#x524D;&#x51E0;&#x4E2A;&#x5B9A;&#x4E49;&#x4E2D;&#x7684;&#x76EE;&#x7684;&#x7C7B;&#x4F3C;&#xFF0C;<span class="katex"><span class="katex-mathml"><math><semantics><mrow><msub><mi>T</mi><mi>S</mi></msub><mo>&#x2260;</mo><msub><mi>T</mi><mi>T</mi></msub></mrow><annotation encoding="application/x-tex">T_S \neq T_T</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height:0.716em;"></span><span class="strut bottom" style="height:0.9309999999999999em;vertical-align:-0.215em;"></span><span class="base textstyle uncramped"><span class="mord"><span class="mord mathit" style="margin-right:0.13889em;">T</span><span class="msupsub"><span class="vlist"><span style="top:0.15em;margin-right:0.05em;margin-left:-0.13889em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle cramped mtight"><span class="mord mathit mtight" style="margin-right:0.05764em;">S</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span><span class="mrel">&#x2260;</span><span class="mord"><span class="mord mathit" style="margin-right:0.13889em;">T</span><span class="msupsub"><span class="vlist"><span style="top:0.15em;margin-right:0.05em;margin-left:-0.13889em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle cramped mtight"><span class="mord mathit mtight" style="margin-right:0.13889em;">T</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span></span></span></span> &#x4E14;<span class="katex"><span class="katex-mathml"><math><semantics><mrow><msub><mi>y</mi><mi>S</mi></msub></mrow><annotation encoding="application/x-tex">y_S</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height:0.43056em;"></span><span class="strut bottom" style="height:0.625em;vertical-align:-0.19444em;"></span><span class="base textstyle uncramped"><span class="mord"><span class="mord mathit" style="margin-right:0.03588em;">y</span><span class="msupsub"><span class="vlist"><span style="top:0.15em;margin-right:0.05em;margin-left:-0.03588em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle cramped mtight"><span class="mord mathit mtight" style="margin-right:0.05764em;">S</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span></span></span></span>&#x548C;<span class="katex"><span class="katex-mathml"><math><semantics><mrow><msub><mi>y</mi><mi>T</mi></msub></mrow><annotation encoding="application/x-tex">y_T</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height:0.43056em;"></span><span class="strut bottom" style="height:0.625em;vertical-align:-0.19444em;"></span><span class="base textstyle uncramped"><span class="mord"><span class="mord mathit" style="margin-right:0.03588em;">y</span><span class="msupsub"><span class="vlist"><span style="top:0.15em;margin-right:0.05em;margin-left:-0.03588em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle cramped mtight"><span class="mord mathit mtight" style="margin-right:0.13889em;">T</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span></span></span></span>&#x90FD;&#x662F;&#x4E0D;&#x53EF;&#x89C2;&#x6D4B;&#x7684;</p>
<p>&#x81EA;&#x5B66;&#x805A;&#x7C7B;&#xFF08;STC&#xFF09;&#x548C;&#x8F6C;&#x79FB;&#x5224;&#x522B;&#x5206;&#x6790;&#xFF08;TDA&#xFF09;&#x7B97;&#x6CD5;&#x5206;&#x522B;&#x63D0;&#x51FA;&#x6765;&#x8F6C;&#x79FB;&#x805A;&#x7C7B;&#x548C;&#x8F6C;&#x79FB;&#x964D;&#x7EF4;&#x95EE;&#x9898;&#x3002;</p>
<h3 id="&#x8FC1;&#x79FB;&#x7279;&#x5F81;&#x8868;&#x793A;&#x7684;&#x77E5;&#x8BC6;"><a name="&#x8FC1;&#x79FB;&#x7279;&#x5F81;&#x8868;&#x793A;&#x7684;&#x77E5;&#x8BC6;" class="anchor-navigation-ex-anchor" href="#&#x8FC1;&#x79FB;&#x7279;&#x5F81;&#x8868;&#x793A;&#x7684;&#x77E5;&#x8BC6;"><i class="fa fa-link" aria-hidden="true"></i></a>1.5.1. &#x8FC1;&#x79FB;&#x7279;&#x5F81;&#x8868;&#x793A;&#x7684;&#x77E5;&#x8BC6;</h3>
<p><code>dai</code>&#x7B49;&#x4EBA;&#x7814;&#x7A76;&#x4E86;&#x4E00;&#x79CD;&#x81EA;&#x5B66;&#x805A;&#x7C7B;&#xFF08;STC&#xFF09;&#xFF0C;&#x501F;&#x52A9;&#x6E90;&#x57DF;&#x4E2D;&#x5927;&#x91CF;&#x672A;&#x6807;&#x8BB0;&#x6570;&#x636E;&#xFF0C;&#x5BF9;&#x76EE;&#x6807;&#x57DF;&#x4E2D;&#x7684;&#x5C11;&#x91CF;&#x672A;&#x6807;&#x8BB0;&#x6570;&#x636E;&#x8FDB;&#x884C;&#x805A;&#x7C7B;&#x3002;&#x5B83;&#x7684;&#x76EE;&#x6807;&#x51FD;&#x6570;&#x5982;&#x4E0B;&#x8868;&#x793A;
<img src="../images/1619009110197.png" alt="1619009110197"></p>
<blockquote>
<p>Z&#x8868;&#x793A;<span class="katex"><span class="katex-mathml"><math><semantics><mrow><msub><mi>X</mi><mi>S</mi></msub></mrow><annotation encoding="application/x-tex">X_S</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height:0.68333em;"></span><span class="strut bottom" style="height:0.83333em;vertical-align:-0.15em;"></span><span class="base textstyle uncramped"><span class="mord"><span class="mord mathit" style="margin-right:0.07847em;">X</span><span class="msupsub"><span class="vlist"><span style="top:0.15em;margin-right:0.05em;margin-left:-0.07847em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle cramped mtight"><span class="mord mathit mtight" style="margin-right:0.05764em;">S</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span></span></span></span>&#x548C; <span class="katex"><span class="katex-mathml"><math><semantics><mrow><msub><mi>X</mi><mi>T</mi></msub></mrow><annotation encoding="application/x-tex">X_T</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height:0.68333em;"></span><span class="strut bottom" style="height:0.83333em;vertical-align:-0.15em;"></span><span class="base textstyle uncramped"><span class="mord"><span class="mord mathit" style="margin-right:0.07847em;">X</span><span class="msupsub"><span class="vlist"><span style="top:0.15em;margin-right:0.05em;margin-left:-0.07847em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle cramped mtight"><span class="mord mathit mtight" style="margin-right:0.13889em;">T</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span></span></span></span>&#x7684;&#x5171;&#x4EAB;&#x7279;&#x5F81;&#x7A7A;&#x95F4;&#xFF0C;I&#x8868;&#x793A;&#x4E24;&#x4E2A;&#x53D8;&#x91CF;&#x4E4B;&#x95F4;&#x7684;&#x4E92;&#x4FE1;&#x606F;&#xFF0C;<span class="katex"><span class="katex-mathml"><math><semantics><mrow><mover accent="true"><mrow><msub><mi>X</mi><mi>T</mi></msub></mrow><mo>&#x20D7;</mo></mover></mrow><annotation encoding="application/x-tex">\vec{X_T}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height:0.9667699999999999em;"></span><span class="strut bottom" style="height:1.1167699999999998em;vertical-align:-0.15em;"></span><span class="base textstyle uncramped"><span class="mord accent"><span class="vlist"><span style="top:0em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="mord textstyle cramped"><span class="mord"><span class="mord mathit" style="margin-right:0.07847em;">X</span><span class="msupsub"><span class="vlist"><span style="top:0.15em;margin-right:0.05em;margin-left:-0.07847em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle cramped mtight"><span class="mord mathit mtight" style="margin-right:0.13889em;">T</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span></span></span><span style="top:-0.25233em;margin-left:0em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="accent-body accent-vec"><span>&#x20D7;</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span></span></span>&#x662F;<span class="katex"><span class="katex-mathml"><math><semantics><mrow><msub><mi>X</mi><mi>T</mi></msub></mrow><annotation encoding="application/x-tex">X_T</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height:0.68333em;"></span><span class="strut bottom" style="height:0.83333em;vertical-align:-0.15em;"></span><span class="base textstyle uncramped"><span class="mord"><span class="mord mathit" style="margin-right:0.07847em;">X</span><span class="msupsub"><span class="vlist"><span style="top:0.15em;margin-right:0.05em;margin-left:-0.07847em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle cramped mtight"><span class="mord mathit mtight" style="margin-right:0.13889em;">T</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span></span></span></span> &#x5BF9;&#x5E94;&#x7684;&#x7C07;</p>
</blockquote>
<p>&#x6211;&#x4EEC;&#x5219;&#x901A;&#x8FC7;&#x4E00;&#x4EE5;&#x4E0B;&#x7684;&#x4F18;&#x5316;&#x51FD;&#x6570;&#x5B66;&#x4E60;<span class="katex"><span class="katex-mathml"><math><semantics><mrow><mover accent="true"><mrow><msub><mi>X</mi><mi>T</mi></msub></mrow><mo>&#x20D7;</mo></mover></mrow><annotation encoding="application/x-tex">\vec{X_T}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height:0.9667699999999999em;"></span><span class="strut bottom" style="height:1.1167699999999998em;vertical-align:-0.15em;"></span><span class="base textstyle uncramped"><span class="mord accent"><span class="vlist"><span style="top:0em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="mord textstyle cramped"><span class="mord"><span class="mord mathit" style="margin-right:0.07847em;">X</span><span class="msupsub"><span class="vlist"><span style="top:0.15em;margin-right:0.05em;margin-left:-0.07847em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle cramped mtight"><span class="mord mathit mtight" style="margin-right:0.13889em;">T</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span></span></span><span style="top:-0.25233em;margin-left:0em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="accent-body accent-vec"><span>&#x20D7;</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span></span></span>
<img src="../images/1619009611933.png" alt="1619009611933"></p>
<p><code>Wang</code>&#x7B49;&#x4EBA;&#x63D0;&#x51FA;&#x4E86;&#x4E00;&#x79CD;TDA&#x7B97;&#x6CD5;&#x6765;&#x89E3;&#x51B3;&#x8F6C;&#x79FB;&#x4F4D;&#x6570;&#x7EA6;&#x51CF;&#x95EE;&#x9898;&#x3002;&#x5B83;&#x9996;&#x5148;&#x5E94;&#x7528;&#x805A;&#x7C7B;&#x65B9;&#x6CD5;&#x4E3A;&#x76EE;&#x6807;&#x672A;&#x6807;&#x8BB0;&#x6570;&#x636E;&#x751F;&#x6210;&#x4F2A;&#x6807;&#x7B7E;&#xFF0C;&#x7136;&#x540E;&#x5728;&#x5BF9;&#x76EE;&#x6807;&#x6570;&#x636E;&#x548C;&#x6709;&#x6807;&#x8BB0;&#x7684;&#x6E90;&#x6570;&#x636E;&#x8FDB;&#x884C;&#x964D;&#x7EF4;&#x3002;&#x4E24;&#x4E2A;&#x6B65;&#x9AA4;&#x8FED;&#x4EE3;&#x8FDB;&#x884C;&#xFF0C;&#x4F7F;&#x5F97;&#x76EE;&#x6807;&#x6570;&#x636E;&#x627E;&#x5230;&#x6700;&#x4F73;&#x5B50;&#x7A7A;&#x95F4;</p>
<h2 id="&#x8F6C;&#x79FB;&#x754C;&#x9650;&#x548C;&#x8D1F;&#x8F6C;&#x79FB;"><a name="&#x8F6C;&#x79FB;&#x754C;&#x9650;&#x548C;&#x8D1F;&#x8F6C;&#x79FB;" class="anchor-navigation-ex-anchor" href="#&#x8F6C;&#x79FB;&#x754C;&#x9650;&#x548C;&#x8D1F;&#x8F6C;&#x79FB;"><i class="fa fa-link" aria-hidden="true"></i></a>1.6. &#x8F6C;&#x79FB;&#x754C;&#x9650;&#x548C;&#x8D1F;&#x8F6C;&#x79FB;</h2>
<p>&#x6211;&#x4EEC;&#x9700;&#x8981;&#x8BA4;&#x8BC6;&#x5230;&#x8FC1;&#x79FB;&#x5B66;&#x4E60;&#x7684;&#x5C40;&#x9650;&#x6027;</p>
<ul>
<li><code>mahmud</code> &#x548C; <code>Ray</code>&#x4F7F;&#x7528; Kolmogorov &#x590D;&#x6742;&#x5EA6;&#x5206;&#x6790;&#x4E86;&#x8FC1;&#x79FB;&#x5B66;&#x4E60;&#x4E2D;&#x7684;&#x60C5;&#x51B5;&#xFF0C;&#x5E76;&#x4F7F;&#x7528;&#x5B83;&#x6765;&#x5EA6;&#x91CF;&#x4EFB;&#x52A1;&#x4E4B;&#x95F4;&#x7684;&#x76F8;&#x5173;&#x6027;</li>
<li><code>Eaton</code>&#x63D0;&#x51FA;&#x4E86;&#x901A;&#x8FC7;&#x5C06;&#x5B66;&#x4E60;&#x7684;&#x6E90;&#x6A21;&#x578B;&#x6620;&#x5C04;&#x5230;&#x56FE;&#x4E2D;&#xFF0C;&#x8BA9;&#x6E90;&#x4EFB;&#x52A1;&#x4E4B;&#x95F4;&#x7684;&#x5173;&#x7CFB;&#x6765;&#x5EA6;&#x91CF;&#x53EF;&#x8FC1;&#x79FB;&#x6027;</li>
</ul>
<h2 id="&#x603B;&#x7ED3;"><a name="&#x603B;&#x7ED3;" class="anchor-navigation-ex-anchor" href="#&#x603B;&#x7ED3;"><i class="fa fa-link" aria-hidden="true"></i></a>1.7. &#x603B;&#x7ED3;</h2>
<ul>
<li>&#x672A;&#x6765;&#x5B9A;&#x4E49;&#x57DF;&#x548C;&#x4EFB;&#x52A1;&#x4E4B;&#x95F4;&#x7684;&#x53EF;&#x8FC1;&#x79FB;&#x6027;&#xFF0C;&#x8FD8;&#x9700;&#x5B9A;&#x4E49;&#x5EA6;&#x91CF;&#x57DF;&#x6216;&#x4EFB;&#x52A1;&#x4E4B;&#x95F4;&#x76F8;&#x4F3C;&#x6027;&#x7684;&#x6807;&#x51C6;</li>
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